polygons - wordpress.com of one interior angle of a convex polyon? e a)108 b)120 c)135 d)140 e)145...

PolygonsTest Bank

Ramazan ŞahinMuhammer Taşkıran

Cüneyt Kılıç

MODULAR SYSTEM

1. Introduction to Polygons.........................................

2. Quadrilaterals............................................................

3. Parallelograms............................................................

4. Rectangles....................................................................

5. Rhombi....................................................................

6. Squares.........................................................................

7. Trapezoids....................................................................

8. Kites..............................................................................

9. Answers to Tests........................................................

CONTENTS

Introduction to Polygons Assignment Test

Polygons

011. What is the number of diagonals of a convex

12-gon?A

A) 54 B) 44 C) 35 D) 27 E) 20

8. In a convex polygon, the ratio of the sum of the

measures of all exterior angles to the sum of the

measures of all interior angles is .

What is the number of the sides of the polygon?E

A) 12 B) 9 C) 8 D) 6 E) 5

6. The sum of the measures of the interior angles ofa convex polygon is 1260°.

Which of the following is the number of sides ofthe polygon?

CA) 12 B) 10 C) 9 D) 8 E) 7

7. Which one of the following cannot be measureof the largest interior angle in a convexnonagon?

BA) 145° B) 139° C) 150° D) 141° E) 152°

2. The number of diagonals of a convex polygonis equal to four times the number of the sides.

What is the number of the sides of the polygon?C

A) 14 B) 12 C) 11 D) 9 E) 8

3. In a convex polygon, the ratio of the number of

diagonals drawn from one vertex to the number of all

diagonals is

What is the number of the sides of the polygon?A

A) 9 B) 10 C) 12 D) 15 E) 18

4. The diagonals drawn through one vertex of aconvex polygon divides the polygon into 9 triangles.

What is the number of the sides of the polygon?C

A) 9 B) 10 C) 11 D) 12 E) 15

5. The number of diagonals of a convex polygonis 65.

Find the number of sides of the polygon.B

A) 10 B) 13 C) 16 D) 20 E) 26

Polygons Assignment Test 019. In the figure,

m(ëA) = 120°,

m(ëE) = 140°,

m(FéDC) = 80°, and

m(CéBH) = 70°

What is m(DéCB) = x in degrees?A

A) 70 B) 75 C) 80 D) 85 E) 90

F

A B

CD

E

H

120°

140°

80°

70°

x

10. In a convex pentagon, the measures of the exteriorangles are proportional to 2, 3, 4, 5, and 6.

What is the measure of the smallest interiorangle of the pentagon?

DA) 144° B) 108° C) 96° D) 72° E) 48°

11. The measure of one interior angle of a regularpolygon is 140°.

How many sides does this polygon have?D

A) 12 B) 11 C) 10 D) 9 E) 8

12. In a regular polygon, the measure of one interiorangle is three times the measure of one exteriorangle.

Find the number of sides of the polygon.B

A) 6 B) 8 C) 9 D) 10 E) 12

14. The difference of the measures of one interior angleand one exterior angle of a regular polygon is 132°.

How many diagonals does the polygon have?B

A) 24 B) 90 C) 77 D) 54 E) 114

15. Which one of the following cannot be themeasure of one interior angle of a convexpolyon?

EA) 108° B) 120° C) 135° D) 140° E) 145°

16. The length of the one side of a regular hexagonis 6 cm.

What is the radius of the inscribed circle of thehexagon ?

B

A) 6 B) 3ñ3 C) 5 D) 4 E) 2ñ3

13.

According to the figure, what is x in degrees?B

A) 10 B) 15 C) 18 D) 20 E) 30

x

3x

2x2x

4x

01

Introduction to Polygons Assignment Test

Polygons

021. In the figure,

ABCDE is a pentagonand [EC] ⊥ [HB].

What is m(HéBC) = x in degrees?B

A) 15 B) 18 C) 24 D) 30 E) 36

A B

C

D

EH

x

2. In the figure,ABCD is a square andEAB is an equilateraltriangle.

What is m(CéEB) = x in degrees?D

A) 45 B) 60 C) 70 D) 75 E) 80

E

A B

D C

x

6. In the figure,ABCD... is aregular convexpolygon,

P, C, D and P, B, Aare collinearpoints, and

m(ëP) = 36°.

What is the number of sides of the polygon?A

A) 5 B) 6 C) 8 D) 9 E) 10

A

B

C DP36°

3. In the figure,ABCDEF is a regularhexagon.

What is m(EéAD) = x in degrees?C

A) 15 B) 25 C) 30 D) 36 E) 45

A B

CF

DE

x

4. In the figure,ABCDE is a regularpentagon and EFD isan equilateral triangle.

What is m(FéCB) = x in degrees?C

A) 30 B) 36 C) 42 D) 60 E) 66

A B

C

D

E

F

x

5. In the figure,ABCDE is a regularpentagon, [BD] is adiagonal and [AF] isan angle bisector.

What is m(HéBC) = x in degrees?C

A) 60 B) 56 C) 54 D) 52 E) 48

A B

C

D

E F

x

Polygons Assignment Test 02

9. In the figure,ABCDE is a regularpentagon and[DH] ⊥ [AB].

What is m(HéDB) = x in degrees?C

A) 10 B) 15 C) 18 D) 20 E) 25

A B

C

D

E

H

x

10. In the figure,ABCDEF is a regularhexagon and

ABH is an equilateraltriangle.

What is m(GéHB) = x in degrees?D

A) 75 B) 70 C) 65 D) 60 E) 45

A B

C

DE

F

GHx

12. In the figure,

ABCDEF is a regularhexagon and|DC| = 2 cm.

What is the perimeter of the triangle EAC?D

A) 12ñ3 B) 9ñ3 C) 9 D) 6ñ3 E) 6

A B

C

DE

F

2

11. In the figure,

ABCDEF is a regularhexagon and

|EC| = 6ñ3 cm.

What is the perimeter of the hexagon?E

A) 72 B) 60 C) 54 D) 48 E) 36

A B

C

DE

F

6ñ3

7. In the figure,ABCDEF is a regularhexagon and

EHGD is a square.

What is m(FéHE) = x in degrees?D

A) 60 B) 65 C) 70 D) 75 E) 80

A B

C

DE

F

H G

x

8. In the figure,ABCDE is a regularpentagon,[EF] ⊥ [FB] and

m(FéBC) = 49°.

What is m(DéEF) = x in degrees?A

A) 5 B) 10 C) 18 D) 20 E) 24

A B

C

D

E

F

49°

x

Quadrilaterals Assignment Test

Polygons

03

2.

According to the given information in the figure

what is m(CéBG) = x in degrees?A

A) 50 B) 60 C) 65 D) 70 E) 80

100°

110°

80°

A B

C

D

E

F G

x

1. In the figure,

m(DéAE) = 80°,

m(CéDA) = 130°,andm(CéBE) = 110°.

What is m(DéCB) = x in degrees?C

A) 100 B) 90 C) 80 D) 70 E) 60

A B E

D

C

130°

80° 110°

x

5. In the figure,ABCD is a quadrilateral,

m(ëA) = 90°, and

Find m(ëC) = c in degrees.D

A) 60 B) 70 C) 80 D) 90 E) 100

c

d

b

A B

C

D

4. In the figure,

m(ëD) = 70°,

m(AéBE) = 50°. and

m(ëA) = m(ëC).

What is the degree measure of the angle A?D

A) 60 B) 70 C) 75 D) 80 E) 85

A B

C

D

70°

50°

E

3. In the figure,[DP and [CPare anglebisectors.

Find the measure of the angle DPC in degrees.A

A) 55 B) 50 C) 45 D) 40 E) 35

P

AB

C

D

FE 130°

120° 6. The measures of interior angles of a quadrilateralare proportional to 3x, , 4x and .

What is the measure of the smallest exteriorangle of the quadrilateral?

DA) 108o B) 96o C) 84o D) 72o E) 60o


9. In the figure,

m(EéAD) = a,

m(ëB) = b,

m(BéCF) = c,

m(ëD) = d, and

b + d = 115°.

Find the value of the sum a + c in degrees.D

A) 65 B) 85 C) 105 D) 115 E) 135

A

B

C

D

a

b

c

d

EF

7. In the figure,

m(ëA) = m(ëC) = 90°,

[BE] is an anglebisector and

m(ëD) = 110°.

What is m(BéEC) = x in degrees?C

A) 35 B) 45 C) 55 D) 60 E) 65

110°

A

B

C

DE

x

10. In the figure,[CE] ⊥ [EB],

m(ëA) = 70°,

m(ëD) = 120°, and

m(EéBA) = 50°.

What is m(DéCE) = x in degrees?A

A) 30 B) 35 C) 40 D) 45 E) 50

E

C

D

A

B50°

70°

120°

x

8. In the figure,

m(AéBC) = 72°,

m(BéCE) = 2α,

m(BéAD) = 3a, and

m(AéDE) = 60°.

What is the value of αα?E

A) 30 B) 36 C) 40 D) 45 E) 48

A

B

CE D

60°2a

3a

72°

11.

In the figure, a + c + d = 272°.What is the degree measure of the angle ABC?

BA) 102 B) 92 C) 86 D) 82 E) 72

A

B

C

D

a

d

c

12. In the figure,ABCD is a quadrilateral,

|EF| = |BF|,

m(ëA) = m(ëC) = 90°,and m(ëD) = 110°.

What is m(EéFC) = x in degrees?A

A) 140 B) 130 C) 120 D) 110 E) 100

A

B

C

D

F

E

110°

x


Polygons

044. In the figure,

[BP] are [CP] areangle bisectors,

m(ëA) = 75°, and

m(ëD) = 95°.

\

What is m(CéPB) = x in degrees?E

A) 75 B) 80 C) 85 D) 90 E) 95

A B F

EC

D

95°

75°

Px

3. In the figure,[BP] and [DP] areangle bisectors,

m(ëC) = 110°, and

m(BéPD) = 165°.

What is m(ëA) = x in degrees?A

A) 80 B) 75 C) 70 D) 65 E) 60

A

B

C

D

165°

110°

Px

5. In the figure,[DP] and [CP] areangle bisectors,

m(ëA) = 90°, and

m(DéPC) = 110°.

What is m(CéBE) = x in degrees?B

A) 40 B) 50 C) 60 D) 70 E) 80

A B

C

D

110°

P

E

x

1. In the figure,

[BE] and [CE] areangle bisectors,

m(ëA) = 70°, and

m(ëD) = 120°.

What is m(CéEB) = x in degrees?D

A) 80 B) 85 C) 90 D) 95 E) 100

A B

E

CD

120°

70°

x

2. In the figure,

ABCD is a

quadrilateral,

[AP] and [CP areangle bisectors,

m(ëB) < 90°,

m(ëD) = 105°, and

m(AéPK) = 25°

Find m(AéBC) = x in degrees.D

A) 70 B) 65 C) 60 D) 55 E) 50

A B

P

C

D105°

K25°

x

6. In the figure,

[AK], [BK], [CP]

and [DP] are angle

bisectors, and

m(AéKB) = 105°.

Find m(DéPC) = x in degrees.C

A) 60 B) 70 C) 75 D) 80 E) 85

P

KA

B

C

D

105°

x


8. In the figure,[AP] ve [CP] areanglebisectors,

[PA] ⊥ [PC],

and

m(AéDC) = 140°.

What is the degree measure of m(FéBE) = x?A

A) 40 B) 45 C) 50 D) 60 E) 70

140°

A B

C

E

F

P

D

x

7. In the figure,[BE] and [CF]are anglebisectors,

m(ëA) = α,

m(ëD) = θ,

m(EéHC) = 80°,and θ – α = 20°.

What is the value of θθ in degrees?D

A) 80 B) 90 C) 100 D) 110 E) 120

B

C

D

80°

H

Eq

A

F

a

10. In the figure,

[AE] is an anglebisector,

[BC] ⊥ [DC],

|CE| = |FE|,

m(ëE) = 50°, and

m(ëB) = 65°.

What is m(AéDC) = x in degrees?B

A) 100 B) 105 C) 110 D) 115 E) 120

65°

50°A

B

E

CD

F

x

9. In the figure,

m(DéAB) = 90°,

m(DéCB) = 90°,

[BE] is an anglebisector,

[AH] ⊥ [BE], and

m(DéAH) = 40°.

Find m(DéEH) = x in degrees.B

A) 140 B) 130 C) 120 D) 110 E) 100

A

B

C

E

D

H40°

x

12. In the figure,[AK], [BP], [CP]and [DK] areangle bisectors,and m(BéEK) = 105°

What is m(CéFK) = x in degrees?B

A) 80 B) 75 C) 70 D) 65 E) 60

P

B

AK

C

D

105°E

Fx

11. In the figure,

|AB| = |AD| = |BC|,

m(ëA) = 60°, and

m(ëC) = 50°.

Find m(AéDC) = x in degrees.C

A) 80 B) 100 C) 110 D) 120 E) 130

A B

CD

60°

50°x


Polygons

05

Test 5

3. In the figure,

[AC] ⊥ [BD],

|AE| = y,

|ED| = x,

|AB| = 5 cm,

|DC| = 7 cm, and

x2 + y2 = 58.

Find the value of |BC| in cm.D

A) 2 B) 3 C) 2ñ3 D) 4 E) 2ñ5

y

x

5

A

B

C

D

E

7

4. In the figure,P, K, L, N are themidpoints of thesides where they lie,

|PK| = 3x + 1, and

|NL| = 5x – 3

How many cm is |PK|?A

A) 7 B) 6 C) 5 D) 3 E) 2

5. In the figure,[DA] ⊥ [AB],

[DC] ⊥ [BC],

|DC| = 6 cm,

|AD| = 8 cm,

|AB| = y,

|BC| = x, and

x – y = 4 cm.

What is the value of the ratio ?E

A

B

C

D

6

8

x

y

6. In the figure,

[AC] ⊥ [BD]

|BC| = 6ñ2 cm,

|AD| = 2ñ7 cm,

|AB| = a,

|DC| = c, and

What is the value of a?E

A) ò10 B) 2ò10 C) 7 D) 8 E) 3ò10

A

B

C

D

2ñ7

6ñ2

c

a

2. In the figure,

m(ëA) = m(ëC) = 90°,

|BC| = 8 cm,

|DC| = 6 cm, and

|AD| = 7 cm.

What is |AB| = x in cm?E

A) 9 B) 8 C) 2ò15 D) 2ò13 E) ò51

A

B

C

D

7 6

8x

1. In the figure,

[AC] ⊥ [BD],

|AB| = 3ñ5 cm,

|DC| = ò61 cm,and |BC| = 5 cm.

What is the value of |AD| = x in cm?B

A) 10 B) 9 C) 8 D) 7 E) 6

A

BD

C

E

ò61 5

3ñ5x


9. In the figure,[AC] ⊥ [BD],

|AE| = |ED|,

|EF| = 4 cm,

|DC| = 3 cm, and

|AB| = 9 cm.

What is |BC| = x in cm?C

A) ò21 B) 2ñ6 C) ò26 D) 3ñ3 E) ò29

34

FA

B

C

D

E

9x

10. In the figure,

m(ëA) = m(ëC) = 90°,

m(ëD) = 120°,

|AD| = 12 cm,

|AE| = 4 cm,

|EF| = 8 cm, and

|EB| = |FB|.

Find the length of FC in cm.A

8

4

120°12

x

A

B

C

D

E

F

8. In the figure,[AC] and [BD] arediagonals, |AN| = |NB|,

|AP| = |PD|,

|DK| = |KC|,

|CT| = |TB|, and

|AC| + |BD| = 24.

What is the perimeter of the quadrilateral PNTK?C

A) 48 B) 36 C) 24 D) 18 E) 12

A B

C

DK

P

N

T

7. In the figure

AC| = |BD|.

What is the type of the quadrilateral formed byjoining the midpoints of the sides of ABCD?

DA) Square B) Rectangle C) Trapezoid

D) Rhombus E) Kite

A

B

C

D

11. In the figure,

[AD] ⊥ [DC],

[AE] ⊥ [BC,]

|CE| = |EB|,

|AD| = 2ò11 cm,

and |DC| = 6 cm.

What is |AB| = x in cm?C

A) 10 B) 9 C) 4ñ5 D) 6ñ2 E) 8

2ò11

A

B

CD

E

6

x

12. In the figure,[AB] ⊥ [BC],

|AB| = ñ3 cm,

|BC| = 1 cm,

|AD| = 2 cm, and

|DC| = 2 cm.

What is the degree measure of the angle BCD?B

A) 105 B) 120 C) 135 D) 145 E) 150

A

D

C

Bñ3

2

2

1

Parallelograms Assignment Test

Polygons

06

Test 6

2. In the figure,ABCD is aparallelogram,

m(DéAE) = 25°, and

m(EéBC) = 30°.

What is m(AéEB) = x in degrees?D

A) 70 B) 65 C) 60 D) 55 E) 50

A B

CD

25° 30°

E

x5. In the figure,

ABCD is aparallelogram,

[AH] ⊥ [BC], and

m(DéCB) = 117°.

What is m(HéAB) = x in degrees?E

A) 63 B) 43 C) 37 D) 33 E) 27

A B

CD

H117°

x


m(ëA) = 5x, and

m(ëB) = 7x.

What is x in degrees?C

A) 20 B) 18 C) 15 D) 12 E) 10

A B

CD

5x 7x


|DE| = |DF|,

m(AéBD) = 20°.

Find the degree measure of the angle DFE.A

A) 80 B) 75 C) 70 D) 65 E) 60

A B

CD E

F

20°


m(PéDC) = 30°,

m(PéBC) = 10°, and

m(DéPB) = 70°.

Find m(DéAB) = x in degrees.B

A) 100 B) 110 C) 120 D) 130 E) 140

A B

CD 30°

10°

70°

P

x


|AE| = |AB|,

m(EéAB) = 80°, and

m(EéBC) = 10°.

What is m(DééAE) = x in degrees?E

A) 10 B) 20 C) 30 D) 35 E) 40

A B

CD E

x80°

10°


ABCD is a parallelogram,

[BE] is an anglebisector, and

m(ëD) = 108°

What is m(CéEB) = x in degrees?C

A) 36 B) 48 C) 54 D) 60 E) 64

A B

CD Ex

108°

12. In the figure,ABCD is a pa ra l l e log ram,[BE] is an anglebisector, |AB| = |BD|, and

m(AéDB) = 70°.

What ism(B ééEC) = x in degrees?B

A) 80 B) 75 C) 70 D) 65 E) 60

A B

CD

70°x

E

8. In the figure,ABCD is a parallelogram,

m(DéCE) = 32°, and

m(EéFB) = 162°.

Find m(CéEF) = x in degrees.D

A) 40 B) 45 C) 48 D) 50 E) 52

A B

CD32°

162°

E

F

x


A, B, and F arecollinear points,

|AF| = |AE|, and

m(AéED) = 42°

Find the degree measure of the angle CEF.A

A) 69 B) 67 C) 65 D) 60 E) 59

A B

CD

42°

F

E


[DH] ⊥ [BC],

m(DéAE) = m(EéAB),

and m(ëB) = 130°.

Find m(AéEH) = x in degrees.A

A) 115 B) 125 C) 135 D) 145 E) 155

A B

CD

H

130°

E

x

9. In the figure,ABCD is a parallelogram,AED is an equilateral triangle,

and m(ëB) = 70°.

What is m(EéAB) = x in degrees?B

A) 60 B) 50 C) 45 D) 40 E) 30

A B

CD

E

70°x


Polygons

07

Test 7


|DE| = |EA|,

and |AK| = 4 cm.

What is |KC| = x in cm?B

A) 6 B) 8 C) 9 D) 10 E) 12

A B

CD

4

KE

x

6. In the figure,ABCD is aparallelogram,D, F, and E arecollinear points asthe points C, B, and E, |AF| = 8 cm, |FB| = 4 cm, and |BE| = 3 cm.

What is |BC| = x in cm?C

A) 8 B) 7 C) 6 D) 5 E) 4

AB

CD

84

x

E

F3

2. In the figure,ABCD is a parallelogram,[BE] is an anglebisector, |DE| = 4 cm, and

|AB| = 10 cm.

What is|AD| = x in cm?C

A) 10 B) 8 C) 6 D) 5 E) 4

A B

CD E4

10

x


[DE] and [CE] areangle bisectors,

|DE| = 9 cm, and|CE| = 12 cm .

Find |AB| = x in cm.A

A) 15 B) 13 C) 12 D) 10 E) 9

A B

CD

E

9 12

x


[AE] is an anglebisector,

|AB| = 13 cm, and

|AD| = 8 cm.

Find the value of |EC| = x in cm.D

A) 9 B) 8 C) 6 D) 5 E) 4

A B

CD

8

13

F

E

x


[DE] is an anglebisector,

|BC| = 8 cm, and

|EB| = 3 cm.

What is |DC| = x in cm?B

A) 9 B) 11 C) 12 D) 14 E) 15

A B

CD

E 3

8

x


[DE] and [CE] areangle bisectors,

|DE| = 3 cm,

and |EC| = 4 cm.

What is the perimeter of the parallelogram ABCDin cm?

BA) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

3 4

E

9. In the figure,ABCD is a parallelogram,B, C, and E arecollinear points asthe pointsA, F, and E, |AD| = |DF|, |AB| = 10 cm, and|BC| = 7 cm.

What is |EC| = x in cm?A

A B

CD F

E

10

7

x12. In the figure,

ABCD is a parallelogram and

|CE| = |EF| = |FB|.

What is the value of the ratio ?B

A B

CD

K

E

F


[HB] ⊥ [AD],

m(ëD) = 120°, and

|DC| = 4ñ3 cm.

Find the length of |HB| = x in cm.D

A) 12 B) 9 C) 8 D) 6 E) 2ñ3

A B

CD

120°

H

4ñ3

x


|DE| = 4 cm,

|EC| = 8 cm, and

|AF| = 9 cm.

What is |FC| = x in cm?B

A) 5 B) 6 C) 7 D) 8 E) 9

A B

CD

F

E4 8

9

x


[AF] and [DF] areangle bisectors,

|AD| = 4 cm, and

|FE| = 6 cm.

What is P(ABCD) in cm?C

A) 28 B) 26 C) 24 D) 20 E) 16

A B

E

CD

4 6F


Polygons

081. In the figure,

ABCD is a parallelogram,

|AE| = 6 cm,

|EB| = 9 cm, and

|FC| = 10 cm.

What is |AF| = x in cm?C

A) 2 B) 3 C) 4 D) 5 E) 6

A B

CD

E6 9

F

10

x


|AK| = 4ñ2 cm, and|KE| = |EF| = x.

Find the value of x in cm.C

A) 2 B) 3 C) 4 D) 6 E) 8

A B

CD

x

x

F

K

E

4ñ2


|EF| = 6 cm, and|FK| = 2 cm.

What is |KC| = x in cm?C

A) 6 B) 5 C) 4 D) 3 E) 2

x

A B

CD

6

2K

E

F


|AC| = 12 cm, and

|BD| = 10 cm.

What is the value of |AB|2 + |BC|2?C

A) 144 B) 132 C) 122 D) 112 E) 98

A B

CD

E


[EB] ⊥ [AD],

|AF| = 6 cm,

|FD| = 3 cm, and

|DC| = 10 cm.

What is|EF| = x in cm?D

A) 8 B) 6 C) 5 D) 4 E) 3

A B

CDE

3

6

10

Fx

5. In the figure,ABCD is a parallelogram, [AP] and [BP] areangle bisectors,

|AB| = 13 cm,

and |EF| = 3 cm.

Find |BC| = x in cm.E

A) 10 B) 8 C) 7 D) 6 E) 5

A B

CD3

13

P

E F

x


12. In the figure,ABCD is a parallelogram, [EA] ⊥ [AB], [BE] is an anglebisector,

m(AéEB) = 60°.

What is the value of the ratio ?A

A B

CD

60°

E


|DE| = |EC|,

|BF| = |FC|, and

|KN| = 4 cm.

What is |DB| in cm?C

A) 8 B) 10 C) 12 D) 14 E) 16

A B

CD

F

K

N4

E


[AD] ⊥ [BD],

[BH] ⊥ [DC],

|AD| = 6 cm, and |DB| = 8 cm.

What is |BH| in cm?C

A) 3,6 B) 4 C) 4,8 D) 5,2 E) 6,4

A B

CD H

86


|DE| = 9 cm,

|EC| = 9 cm,

|CB| = 10 cm.

If 2|AF| = |FB| and m(DéAB) = 60° then what is |EF| = x in cm?

C

A) 11 B) 5ñ5 C) ó139 D) 5ñ6 E) 13

9 9

A B

10

CD

60°

E

x

F

11. In the figure,G is the centroidof the right triangle ABC,

|BE| = |EG|,

|CM| = |MG|,

|BC| = 12 cm.

Find the perimeter of DEMN in cm.B

A) 12 B) 16 C) 18 D) 20 E) 24

A

D

B C

E M

GN

12


[AE] ⊥ d,

[DF] ⊥ d,

[BH] ⊥ d,

[CG] ⊥ d,

|AE| = 6 cm,

|CG| = 3 cm, and |BH| = 8 cm.

What is |DF| in cm?A

A B

CDE

F

HG

d

6

3


Polygons

09

Test 9

1. In the figure,ABCD is aparallelogram,|DE| = |EB|,

m(DéEB) = 110°,

and m(EéBC) = 100°.

What is the degree measure of the angle ADE?D

A) 10 B) 15 C) 20 D) 30 E) 35

A B

CD

E110°

100°

2. In the figure,ABCD is aparallelogram,[AE] is an anglebisector,[AE] ⊥ [EF], and

m(EéFB) = 130°.

Find the measure of the angle ADE in degrees.A

A) 100 B) 110 C) 120 D) 130 E) 140

A B

CD

F130°

E

3. In the figure,ABCD is aparallelogram,[AF] and [BE] areangle bisectors,|AB| = 17 cm,and |AD|=12cm.

What is |EF| = x in cm?C

A) 10 B) 9 C) 7 D) 6 E) 5

A B

CD

P

12

17

E Fx


[EA] // [DB] // [FC],

|EA| = 5 cm, and

|DB| = 12 cm.

What is |FC| = x in cm?C

A) 5 B) 6 C) 7 D) 8 E) 10

A B

CD

5

12

x

F

E


|AB| = 21 cm,

|FH| = 4 cm, and

|HC| = 6 cm.

What is |DE| = x in cm?E

A) 6 B) 8 C) 9 D) 10 E) 12

A B

CD E

4

6

21

F

H

x

4. In the figure,ABCD is aparallelogram,D, E, and F arecollinear points,

|AE| = |AD|,

m(ëF) = 25°, and

m(EéDC) = 50°.

Find the measure of the angle BCF in degrees.D

A) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

50°

25°

E

F


8. In the figure,ABCD is aparallelogram,|AE| = |EB|,|EF| = 6 cm,|OF| = 4 cm, and

|BC| = 4ò13 cm.

Find |DC| = x in cm.D

A) 10 B) 15 C) 18 D) 20 E) 25

A B

CD

E

O

F6

4 4ò13

x

9. In the figure,ABCD is aparallelogram,[AE], [BE], [CF]and [DF] are anglebisectors,|AB| = 20 cm, and|BC| = 13 cm.

What is |EF| in cm?C

A) 10 B) 8 C) 7 D) 6 E) 3

A B

CD

E

F

20

13

10. In the figure,ABCD is aparallelogram,|BK| = |KC|,|DP| = |PC|,|DE| = 2 ⋅ |AE|,|BF| = 2 ⋅ |AF|.

Find the value of the ratioD

A B

CD

E

F

P

K


m(DéCF) = m(FéCB),|AB| = 15 cm,

|AD| = 9 cm, and

|BD| = 16 cm.

What is |EF| in cm?B

A B

CD

E

F

9

15


|BE| = 2 ⋅ |AE|,

|CF| = 3 ⋅ |FB|,and |KC| = 6 cm.

Find |KE| in cm.C

A) 4 B) 5 C) 6 D) 8 E) 9

A B

CD

K6

F

E

7. In the figure,ABCD is aparallelogram,[EH] ⊥ [DC],|AB| = 25 cm,|BC| = 15 cm, and

|EB| = 5ò13 cm.

What is |EH| = x in cm?B

A) 8 B) 6 C) 5 D) 4 E) 3

A B

CD

E

H

15

25

5ò13

x

Rectangles Assignment Test

Polygons

10

5. In the figure,

ABCD is a

rectangle,

[EF] ⊥ [FC], and

m(DéEF) = 125°.

What is m(FéCB) = x in degrees?E

A) 55 B) 50 C) 45 D) 40 E) 35

A B

CD

125°E

F

x

6. In the figure,

ABCD is a

rectangle,

m(AéBE) = 60°,

|AB| = 12 cm, and

|EB| = 10 cm.

What is |DE| = x in cm?C

A) 5 B) 6 C) 7 D) 8 E) 9

A B

CD

10

E

12

60°

x

2. In the figure,

ABCD is a

rectangle, and

m(AéEB) = 140°.

What is m(DéBC) = x in degrees?D

A) 40 B) 50 C) 60 D) 70 E) 80

A B

CD

x140°

E

3. In the figure,

ABCD is a

rectangle,

|DC| = 6ñ3 cm,

m(DéBC) = 60°.

Find |AD| = x in cm.C

A) 12 B) 8 C) 6 D) 4 E) 3

A B

CD

60°

x

6ñ3

4. In the figure,

ABCD is arectangle and[BE] is an anglebisector.

What is m(DéEB) = x in degrees?B

A) 150 B) 135 C) 120 D) 115 E) 105

A B

CD E

x

1. In the figure,

ABCD is a

rectangle,

|AD| = 8 cm, and|AC| = 17 cm.

What is |AB| = x in cm?A

A) 15 B) 13 C) 12 D) 10 E) 9

A B

CD

x

8 17

Polygons Assignment Test 10Test 107. In the figure,

ABCD is a rectangle,

[BD] ⊥ [CE],

|DE| = 9 cm, and

|EB| = 16 cm.

What is |CE| = x in cm?A

A) 12 B) 10 C) 9 D) 8 E) 6

A B

CD

E

9

16

x

10. In the figure,


[DE] is an anglebisector,

C, B, and E arecollinear points,

|AD| = 8 cm, and

|BE| = 4 cm.

What is |DC| = x in cm?B

A) 10 B) 12 C) 14 D) 15 E) 16

AB

CD

4

8

E

F

x

11. In the figure,


[EH] ⊥ [AB],

|EH| = 3 cm, and

|HB| = 4 cm.

What is |AC| in cm?C

A) 5 B) 8 C) 10 D) 13 E) 15

A B

CD

3

4

E

H

12. In the figure,


|DC| = 12 cm,

|BC| = 20 cm, and

|DE| = 15 cm.

Find |EB| = x in cm.B

A) 15 B) 13 C) 12 D) 10 E) 8

A B

CD

E

15

12

20

x

8. In the figure,


[DK] ⊥ [AC],

[BT] ⊥ [AC],

|AK| = 2 cm, and

|BT| = 4 cm.

What is |KT| = x in cm?E

A) 4 B) 2ñ5 C) 2ñ7 D) 4ñ2 E) 6

A B

CD

K

T

2

x 4

9. In the figure,


|AE| = |ED|,

|FD| = 2 cm, and

|DC| = 5 cm.

Find |BC| = x in cm.B

A) ñ7 B) ò11 C) ò13 D) ò15 E) ò17

A DE

B C

2

F

x

5


Polygons

11

Test 11

1. In the figure,


|DF| = |EC|, and

m(CéEF) = 72°.

What is m(CéAB) = x in degrees?D

A) 18 B) 24 C) 30 D) 36 E) 40

A B

CD

72°

F

E

x

2. In the figure,

[AE] is thebisector of theangle DAF,

|EC| = 13 cm,and |BC| = 5 cm.

Find the length of AB in cm.C

A) 10 B) 9 C) 8 D) 6 E) 5

A B

CD

13

5

E

F x

4. In the figure,

[AF] ⊥ [FE],

m(FéAB) = 45°,

|FC| = 3ñ2 cm,

|EB| = 2ñ2 cm.

What is |AF| = x in cm?D

A) 6 B) 8 C) 9 D) 10 E) 12

A B

CD F

45°

E

2ñ2

3ñ2

x

3. In the figure, ABCDis a rectangle,[AE] ⊥ [EB],

|DE| = 9 cm, and

|BC| = 6 cm.

What is |EC| = x in cm?C

A) 6 B) 5 C) 4 D) 3 E) 2

A B

CD E9 x

6

5. In the figure,

ABCD is a

rectangle,

D, F, and E arecollinear points,

|FB| = |EB|, and

m(FéBE) = 40°.

What is m(EéDC) = x in degrees?D

A) 40 B) 50 C) 60 D) 70 E) 80

A B

CD

40°

E

F

x

6. The ratio of the lengths of the sides of rectangle is

If the perimeter of the rectangle is 42 cm, thenfind the length of one diagonal of the rectangle,in cm.

EA) 9 B) 12 C) 13 D) 14 E) 15



EAB is an equilateraltriangle, and

|EF| = |EC|.

Find the degree measure of the angle FCB.D

A) 15 B) 20 C) 25 D) 30 E) 35

A B

CD E

F

8. In the figure, ABCDis a rectangle,

[CE] is the bisectorof angle C,

|AE| = 4 cm, and|EB| = 5 cm.

Find the perimeter of the rectangle ABCD.E

A) 14 B) 18 C) 20 D) 24 E) 28

A B

CD

4 E 5

10. In the figure,


|BC| = 8 cm,

|EC| = 10 cm, and

|DC| = 21 cm.

What is |DE| = xin cm?C

A) 10 B) 15 C) 17 D) 20 E) 25

A B

CD

E

810x

21

11. In the figure,

ABCD is a

rectangle,

[AE] ⊥ [EB],

|AF| = |FB|,

|DE| = 2 cm, and |BC| = 4 cm.

What is |EF| = x in cm?D

A) 10 B) 8 C) 6 D) 5 E) 4

A B

CD E2

F

4x

12. In the figure,

ABCD is a

rectangle,

m(PéCD) = 25°, and

m(AéPC) = 35°.

What is m(PéAD) = x in degrees?E

A) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

x

25°

35°

P

9. In the figure,


|AD| = |EB|, and

m(AéBE) = 60°.

What is the measure of the angle DCE indegrees?

BA) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

60°

E


Polygons

121. In the figure,

ABCD is a

rectangle,

|BC| = 3 cm,

|AE| = 3 cm, and

|DC| = 8 cm.

What is |EC| in cm?A

A) 10 B) 11 C) 12 D) 13 E) 14

AB

CD

E

8

3

3

F

4. In the figure,


[KN] ⊥ [DC],

|DK| = |KC|,

|EC| = 5 cm, and

|KN| = 9 cm.

What is |BE| = x in cm?C

A) 5 B) 6 C) 8 D) 9 E) 10

A B

CD

5

9

K

E

Nx

2. In the figure,


|AD| = |CE|,

|DE| = |DC|, and

m(AéDE) = 66°.

Find the measure of the angle EBA in degrees.B

A) 5 B) 6 C) 9 D) 10 E) 12

A B

CD

E

66°

3. In the figure,

ABCD is a

rectangle,

|DE| = 6 cm, and

|EC| = 9 cm.

Find the value of the ratio .D

A B

CD

F

E6 9

5. In the figure,


|AE| = |EB|,

|BC| = 9 cm, and

m(CéAB) = 30°.

Find |AF| = x in cm.C

A) 9 B) 8 C) 6 D) 4 E) 3

A B

CD

30°

F

E

9

x

6. In the figure,


|PD| = 2 cm,

|PA| = 8 cm, and

|PC| = 6 cm.

What is |PB| in cm?B

A) 10 B) 4ñ6 C) 3ò10 D) 9 E) 6ñ2

A B

CD

P

62



D, A, and E arecollinear points,

|AE| = |AC|, and

m(CéFB) = 54°.

Find m(AéCD) = x in degrees.E

A) 36 B) 30 C) 24 D) 20 E) 18

AB

CD

E

x

54°F

8. In the figure,


|DE| = |EF| = |FA|,

|BE| = 8 cm, and

|EC| = 3 cm.

What is |AB| = x in cm?B

A) 3 B) 4 C) 5 D) 6 E) 8

A B

CD

F

E

3

8

x

9. In the figure, P isany point in theinterior of therectangle,

|PA| = 9 cm,

|PD| = 10 cm, and

|PC| = 8 cm.

What is |PB| = x in cm?E

A) 4 B) 5 C) 4ñ2 D) 6 E) 3ñ5

A B

CD

10 8

9P

x

10. In the figure,

ABCD is a

rectangle,

|AE| = |ED|,

|AF| = |FB|, and

|PK| = 5 cm.

What is |BD| in cm?B

A) 10 B) 15 C) 18 D) 20 E) 25

E

A B

CD

P

K

F

5

11. In the figure,


m(EéDB) = m(BéDC),

[EF] ⊥ [DB],

|DC| = 16 cm, and

|CB| = 12 cm.

Find |EF| = x in cm.E

A) 5 B) 6 C) 6,5 D) 7 E) 7,5

A B

CD

E

F

x

16

12

12. In the figure, ABCDis a rectangle, [BE]is an anglebisector, and

m(EéAB) = 30°

What is the value of the ratio ?

C

A) 2 B) 2ñ3 C) ñ3 + 1 D) 3 E) ñ3 + 2

A B

CD E

30°

Rhombi Assignment Test

Polygons

13

Test 13

5. In the figure,ABCD is a rhombus,

[AE] ⊥ [DC], and

|DE| = |EC|.

Find m(DéAE) = x in degrees.A

A) 30 B) 35 C) 40 D) 45 E) 60

A

B

C

D

E

x

3. In the figure,ABCD is arhombus,

[BE] ⊥ [AD]

|AE| = 3 cm

|ED| = 2 cm

Find |EB| = x in cm.C

A) 6 B) 5 C) 4 D) 3 E) 2

A B

CD2

3

E

x


[CE] ⊥ [AB],

[CF] ⊥ [AD], and

|CF| = 6 cm.

What is |CE| = x in cm?D

A) 12 B) 9 C) 8 D) 6 E) 3

A B

CD

6

x

F

E


H, A, and B arecollinear points,

[HD] ⊥ [HA],

|BC| = 17 cm, and

|HA| = 8 cm.

What is |HD| = x in cm?B

A) 17 B) 15 C) 13 D) 12 E) 10

H

x

8

17

A

B

C

D

6. The lengths of the diagonals of a rhombus are10 cm and 24 cm.

Find the length of one side of the rhombus.C

A) 10 B) 12 C) 13 D) 15 E) 17

1. In the figure,ABCD is a rhombus

and m(CéDB) = 52°.

What is m(DéAB) = x in degrees?E

A) 52 B) 60 C) 64 D) 72 E) 76

A B

CD

52°

x


ABCD is arhombus,DEC is equilateraltriangle and

m(EéCB) = 10°.

Find the angle EAB in degrees.A

A) 5 B) 10 C) 15 D) 20 E) 25

A B

CD

10°

E


BEFC is asquare, and

m(DéCB) = 108°.

What is m(AéEF) = x in degrees?B

A) 85 B) 81 C) 79 D) 72 E) 69

A B

CD

E

F

108°

x

10. In the figure,ABCD is arhombus, [DB]and [AC] arediagonals,

[HE] ⊥ [AD],

|AH| = 8 cm,

|HD| = 2 cm.

Find |HE| = x in cm.C

A) 2 B) 3 C) 4 D) 2ñ5 E) 5

A B

CD

2

H

8

Ex


m(ëA) = 120°,

[EF] ⊥ [AD],

|AE| = 7 cm, and

|EF| = 4ñ3 cm.

What is |FC| = x in cm?D

A) 6 B) 5 C) 4 D) 3 E) 2

x7

A

B

C

D

120°

E

F4ñ3

11. In the figure,ABCD isa rhombus,

[BH] ⊥ [AD],

|BC| = 10 cm,

|BH| = 8 cm.

Find |BD| = x in cm.C

A) 10 B) 9 C) 4ñ5 D) 5ñ3 E) 2ò17

A B

CD

x 10

8

H


A, C, and E are

collinear points,

|BC| = |CE|, and

m(EéDC) = 32°.

What is m(AéBC) = x in degrees?E

A) 64 B) 60 C) 58 D) 54 E) 52

A B

CD32°

x

E

Rhombi Assignment Test

Polygons

14

Test 14


D, B, and E arecollinear points,

|AD| = 15 cm,

|DB| = 18 cm,and

|BE| = 7 cm.

Find |CE| = x in cm.C

A) 17 B) 19 C) 20 D) 25 E) 30

A B

CD

E

18

7

15

x

2. In the figure,ABCD is arhombus,ECB is anisosceles righttriangle, and

m(DéAB) = 110°.

What is m(EéDC) = x in degrees?B

A) 5 B) 10 C) 15 D) 18 E) 20

A B

CD

E

110°

x


m(ëA) = 100°, and

m(BéEC) = 55°.

Find m(DéBE) = x in degrees.D

A) 30 B) 25 C) 20 D) 15 E) 10

B

A C

D

E

55°100°

x

4. In the figure,ABCD is arhombus,|ED| = |DB|,

m(CéDB) = 36°.

What is m(EéDA) = x in degrees?E

A) 45 B) 50 C) 60 D) 65 E) 72

A B

CD

E

36°x


m(DéEA) = m(AéEB),

m(DéAE) = 30°, and

m(AéBE) = α.

What is m(A ééBE) = αα in degrees?E

A) 50 B) 55 C) 60 D) 65 E) 80

30°

a

A B

CED

6. In the figure,BDEF is arhombus, and


A

A

B CD

EF


ABCD is arhombus,C, D, and Eare collinearpoints, and

m(DéEA) = 55°.

What is m(DéAB) = x in degrees?D

A) 55 B) 60 C) 65 D) 70 E) 75

A

B

C

D

E

55°x

8. In the figure,ABCD is a rhombus,|AE| = |ED|, and|FG| = 1 cm.

Find |BD| in cm.C

A) 4 B) 5 C) 6 D) 8 E) 10

A

B

E

C

DGF

1

9. In the figure,ABCD is a rhombus,[AC] is diagonal,

|FB| = 2 cm, and

|AB| = 5 cm.


D

A B

D C

2

5

E

F


[DE] ⊥ [DC],

|DE| = 4ñ3 cm,

|AE| = 4 cm, and

|EC| = x.

Find |EC| = x in cm.A

A) 12 B) 13 C) 14 D) 16 E) 18

A B

D C

4 E

4ñ3 x

12.

In the figure, ABCD is a rhombus, CBF is an

equilateral triangle, and m(DéFB) = 20°.

What is m(DéAB) = x in degrees?B

A) 30 B) 40 C) 45 D) 50 E) 60

A B

D C

E

F

x

20°

10. In the figure,ABCD is arhombus,[BE] is anangle bisector, [CE] ⊥ [EB], |DF| = |FA|,

m(DéAB) = 70°.

What is m(FéEC) = x in degrees?D

A) 120 B) 125 C) 135 D) 145 E) 160

A B

D C

E

70°

xF

Squares Assignment Test

Polygons

15

Test 15

2. In the figure,ABCD is asquare,

m(DéAE) = 3x, and

m(EéAB) = 2x.

Find the measure of the angle AEC in degrees.B

A) 130 B) 126 C) 124 D) 120 E) 116

A B

CD

3x2x

E

3. In the figure,ABCD is asquare and|BD| = 12 cm.

What is the perimeter of the square in cm?D

A) 48 B) 42 C) 36 D) 24ñ2 E) 24

A B

CD

12


m(AéBE) = 60°, and

|AB| = 4ñ3 cm.

What is |BE| = x in cm?B

A) 10 B) 8 C) 6 D) 5 E) 4

A B

CD

60°

E

4ñ3

x

1. In the figure,ABCD is a square,|AE| = |BC|,

m(CéDE) = 25°.

What is m(EéAB) = x in degrees?C

A) 65 B) 50 C) 40 D) 35 E) 30

A B

CD

E

25°

x

5. In the figure,ABCD is asquare,|BE| = 6 cm, and

|EC| = 2 cm.

Find |AE| = x in cm.D

A) 4ñ3 B) 8 C) 9 D) 10 E) 12

A B

CD

6

2

E

x

6. In the figure,ABCD is asquare,E, D, and C arecollinear points,|ED| = 5 cm, and|DC| = 12 cm.

What is |AE| = x in cm?E

A) 8 B) 9 C) 10 D) 12 E) 13

A B

CD5E

x

12

Polygons Assignment Test 15Test 15

8. In the figure,ABCD is a square,

|DE| = 6 cm,

|EC| = 6 cm, and

[AE] ∩ [BD] = {F}.

What is |FB| = x in cm?E

A) 4ñ2 B) 6 C) 5ñ2 D) 8 E) 8ñ2

A B

CD E6 6

F

x

10. In the figure,ABCD is a square,EAB is an isoscelestriangle, and

|BC| = 6ñ2 cm.

Find the value of the sum |AE| + |EB|.C

A) 6 B) 8 C) 12 D) 15 E) 18

A B

CD

E 6ñ2

9. In the figure,ABCD is a square,[AC] is diagonal ofthe square,|AE| = 2 cm,|EC| = 14 cm.

Find |DE| = x in cm.A

A) 10 B) 9 C) 8 D) 6 E) 5

A B

CD

E2

14x


[EF] ⊥ [AB],

|BC| = 8 cm, and

|DF| = 2ñ2.


A) 3 B) 4 C) 5 D) 6 E) 8

A B

CD

F

x

E

8

2ñ2

12. In the figure,ABCD is a square,[AC] is diagonal ofthe square,|BE| = 2x + 1 cm,|DE| = 3x – 2 cm.

What is the value of x?C

A) 1 B) 2 C) 3 D) 4 E) 5

A B

CD

3x�2

2x+1

E


|AE| = |EB|, and

|DE| = ñ5 cm.

What is the length of one side of the square?A

A B

CD

E

ñ5


Polygons

16

Test 16


[KF] ⊥ [BC],

|BF| = |FC|,

|AE| = 8 cm, and

|EB| = 3 cm,

What is |KF| = x in cm?D

A) 4 B) 5 C) 6 D) 7 E) 8

A B

CD

K

8 E 3

Fx


|AF| = 2 cm,

|FD| = 4 cm.

Find |EA| = x in cm.B

A B

CD

E

F

2

4

x

3. In the figure,ABCD is a squareand EBC is anequilateraltriangle.

What is m(EéAB) = x in degrees?B

A) 80 B) 75 C) 70 D) 60 E) 50

A B

CD

E

x


[EF] ⊥ [AC],

|AF| = 4ñ2 cm, and

|FB| = 2ñ2 cm.

Find |EC| = x in cm.C

A) 4 B) 6 C) 8 D) 10 E) 12

A B

CD

F

E

4ñ2 2ñ2

x


|FB| = |BE|, and

m(AéDE) = 70°.

What is m(DéEF) = x in degrees?B

A) 60 B) 65 C) 70 D) 75 E) 80

A B

CD

F

E

70°

x


[AC] is diagonal ofthe square, and

[AE] is the bisectorof the angle DAC.

Find m(AéEC) = x in degrees.D

A) 102,5 B) 107,5 C) 110 D) 112,5 E) 120

A B

CD E

x


ABCD is a square,

m(DéAF) = 26°,and [FE] is anangle bisector.

What is m(FéEB) = x in degrees?A

A) 148 B) 144 C) 142 D) 138 E) 128

A B

CD F

26° Ex


|DE| = 5 cm, and

|EB| = 1 cm.

Find |BC| = x in cm.A

A B

CD

E

5

1

x


DEFH is a rectangle,

|EF| = 3ñ2 cm, and

|HF| = ñ2 cm.

What is |AC| in cm?D

A) 4ñ2 B) 6 C) 5ñ2 D) 8 E) 6ñ2

A B

CD

FE

H

3ñ2

ñ2


|DE| = |EA|, and

|EB| = 2ñ5 cm.

Find |DC| = x in cm.D

A) 1 B) 2 C) 3 D) 4 E) 5

D A

BC

E

x 2ñ5


|DE| = 2a – 2 cm,

|BE| = a + 4 cm,

|AB| = 8ñ2 cm, and

|EC| = x.

What is |EC| = x in cm?B

A) ñ2 B) 2 C) 2ñ3 D) 4 E) 3ñ2

A B

CD

E

a+4

x

8ñ2

2a�2


|CF| = 2|AE|,

|FB| = 2|CF|,

|DC| = 6 cm, and

|EF| = x.

What is |EF| = x in cm?E

A) 8 B) 9 C)5ñ5 D) 4ñ3 E) 3ñ5

A B

CD

x

6

F

E


Polygons

17

Test 17


[DH] ⊥ [EC],

|EH| = ñ5 cm, and

|HC| = 4ñ5 cm.

What is the length of one side of the squareABCD in cm?

A

A) 10 B) 3ò10 C) 9 D) 6ñ2 E) 8

A B

CD

HE ñ5

4ñ5


|AE| = 7 cm, and

|BC| = 15 cm.


A) 13 B) 15 C) 17 D) 18 E) 20

A B

CD

E

7

x

15

5. In the figure,ABCD is asquare,E, D, and C arecollinearpoints,[EA] ⊥ [AC],|EC| = 12 cm.


A) 6 B) 5ñ2 C) 8 D) 6ñ2 E) 10

A B

DE C

3. In the figure,ABCD is a squareand AED is anequilateraltriangle.

What is m(BéDE) = x in degrees?B

A) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

E

x

4. In the figure,ABCD is asquare,[EF] ⊥ [AC],

[PK] ⊥ [AC],

|AF| = 2ñ2 cm,

|FP| = 4ñ2 cm,

|PC| = 3ñ2 cm.

Find the value of the ratio .D

A B

CD

F

P

E K

2ñ2

4ñ2

3ñ2

2. In the figure,ABCD is asquare andthe triangleEAD isequilateral.

Find m(CéEA) = x in degrees.A

A) 45 B) 40 C) 35 D) 30 E) 25

A B

D

E

C

x

Polygons Assignment Test 17Test 17

8. In the figure,ABCD is asquare,ABFE is arhombus, and

m(EéAB) = 50°.

What is m(AéED) = x in degrees?D

A) 40 B) 50 C) 60 D) 70 E) 80

A B

CD

FE

50°

x


m(EéDC) = 30°,

|FE| = 4 cm,

|AD| = x.

Find |AD| = x in cm?D

A) 2ñ3 B) 2 + 2ñ3 C) 4 + 2ñ3

D) 3 + ñ3 E) 2 + ñ3

A B

CD30°

F

4

E

x


A, E, and C arecollinear points,

|AE| = 8 cm,

|DE| = 6 cm, and

|EB| = 6 cm.

What is |EC| = x in cm?E

A) 2 B) 3 C) ñ6 D) ñ7 E) 2ñ2

A B

CD

x6

68

E


[CF] ⊥ [BE],

|DE| = 3 cm, and

|EA| = 9 cm.

Find |CF| = x in cm.E

A) 3,6 B) 4,8 C) 6,4 D) 7,2 E) 9,6

A B

CD

F

E

3

9

x


[AC] ∩ [BE] = {F},

|DE| = 2 cm, and

|EA| = 6 cm.

Find |EF| = x in cmD

A B

CD

2

E

6F

x


m(DéEB) = 120°, and

|DE| = 10 cm,

What is |EB| = x in cm?C

A) 5 B) 5ñ3 C) 5ñ3 – 5 D) 4ñ3 E) 4ñ3 – 4

A B

CD

120°

10

E x


Polygons

18

2.

In the figure, ABCD is a square, E, A, F, B arecollinear points, [ED] ⊥ [DF], |AF| = 4 cm, and|FB| = 2 cm.

Find |EA| = x in cm.E

A) 4 B) 5 C) 6 D) 8 E) 9

E A F B

CD

4 2x

3. In the figure,ABCD is a square,the triangle DECis equilateral,[EF] ⊥ [AB],and |DC| = 6 cm


A B

CD

E

F

x

6


|AF| = 1 cm,

|EC| = 1 cm, and

|FB| = 7 cm.

What is |EF| = x in cm?A

A) 10 B) 12 C) 13 D) 14 E) 15

A B

CD

1 7

1

F

E

x


|AE| = |EB|,

|AF| = |FD|, and

[FE] // [DK].

What is the value of the ratio ?C

A B

CD

F

E

K

4. In the figure,ABCD is a square,[AC] is a diagonalof the square,|AE| = 2 cm, and

|EB| = 10 cm.

What is |EC| = x in cm?A

A) 14 B) 12 C) 10 D) 9 E) 8

A B

CD

E2 10

x

5. In the figure,

ABCD is a

square,

[EA] ⊥ [EC],

|EA| = 2ñ2 cm,

|AB| = 6 cm.

Find |EC| in cm.C

A) 10 B) 9 C) 8 D) 6 E) 5

A B

CD

E

6

2ñ2


8. In the figure,E, D, and Care collinearpoints,

[EF] ⊥ [FC],

|ED| = 4 cm,

|FA| = 3 cm.

Find the perimeter of the square ABCD in cm?C

A) 24 B) 32 C) 36 D) 40 E) 48

A B

CDE 4

3F


[HF] ⊥ [FE],

|AE| = 2 cm,

|BF| = 6 cm, and

|HC| = 3 cm.

What is |DH| = x in cm?B

A) 8 B) 7 C) 6 D) 5 E) 4

A B

CD

F

H 3

6

2 E

x

7. In the figure, ABCDis a square,

m(EéDB) = 15°, and

|AE| = 2 cm.

What is |EB| = x in cm?D

A) 1 B) 2 C) 2ñ3 D) 2ñ3 – 2 E) 2ñ3 – 3

A B

CD

x2 E

15°

10. In the figure, ABCD

is a square,

[AE] ⊥ [CE],

F is the intersection

point of the

diagonals of the

square, and

|EF| = 4 cm.

What is the length of one side of the square?E

A) 8ñ2 B) 6ñ2 C) 8 D) 6 E) 4ñ2

A B

CD

E

F


E, A, and B arecollinear points,

[ED] ⊥ [DF], and

m(CéDF) = 30°.

What is the measure of the angle FEBin degrees?

BA) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

E

30°

F

12. In the figure, KEFB

is a square,

ABCD is a right

triangle,

P, K, and F are

collinear points, and

Find the measure of the angle.D

A) 30 B) 45 C) 60 D) 75 E) 90

P

AB

CD

K

E F

Trapezoids Assignment Test

Polygons

19

2. In the figure,ABCD is atrapezoid,[DC] // [AB],|DC| = |BC|,

m(AéBD) = 42°.

Find m(DéCB) = x in degrees.D

A) 108 B) 104 C) 100 D) 96 E) 84

A B

CD

42°

x

4. In the figure,

ABCD is a

trapezoid,

|AE| = |ED|,

|BF| = |FC|,

|EF| = 9 cm, and

|DC| = 6 cm.

Find |AB| = x in cm.E

A) 18 B) 16 C) 15 D) 13 E) 12

A B

CD

E F

6

9

x

5. In the figure,

ABCD is a

trapezoid,

[EF] is themedian,

|DC| = c,

|AB| = a,

|KL| = 6 cm, and |EF| = 10 cm.


A

A B

CD

E F

c

a

K L

O

1. In the figure,ABCD is a

trapezoid,

m(ëA) = 3x,

m(ëB) = 4x, and

m(ëC) = 6x.

What is measure of the angle ADC in degrees?B

A) 128 B) 126 C) 120 D) 118 E) 116

A B

CD

3x

6x

4x

3. In the figure, ABCDis a trapezoid,

m(ëA) = 75°,

m(DéBC) = 27°, and

m(DéCB) = 119°.

What is m(AéDB) = x in degrees?B

A) 75 B) 71 C) 69 D) 61 E) 58

A B

CD

27°75°

119°x

6. In the figure,

ABCD is a

trapezoid,|AE| = |ED|,|BF| = |FC|,|DC| = 8 cm,|EP| = 5 cm,

|AB| = a, and |PF| = x.

Find the value of the difference a – x in cm.A

A) 6 B) 5 C) 4 D) 3 E) 2

A B

CD

PE F5

8

x

a


9. In the figure,ABCD is atrapezoid,

m(ëA) = 64°,

m(ëC) = 128°,|BC| = 7 cm,|DC| = 5 cm.

Find |AB| = x in cm.C

A) 14 B) 13 C) 12 D) 10 E) 8

A B

CD

64°

128°

5

7

x

12. In the figure,ABCD is atrapezoid,[DE] and [CF]are angleb i s e c t o r s ,|AD| = 6 cm,|BC| = 5 cm,|AB| = 14 cm.

What is |EF| in cm?C

A) 1 B) 2 C) 3 D) 4 E) 5

A B

CD

E F

6 5

14

10. In the figure,

ABCD is a trapezoid,

|AP| = |PE| = |ED|,

|BN| = |NF| = |FC|,

|AB| = 15 cm, and|DC| = 7 cm.

What is the value of the sum |PN| + |EF| in cm?E

A) 11 B) 14 C) 16 D) 20 E) 22

A B

CD

E F

7

15

P N

7. In the figure, ABCDis a trapezoid,[AE] and [DE] areangle bisectors,|AB| = 18 cm, and|DC| = 10 cm.

What is |AD| = x in cm?D

A) 14 B) 17 C) 24 D) 28 E) 36

A B

CD

E

10

18

x

11. ABCD is a

trapezoid,

m(DéAB) = 30°,

m(AéBC) = 60°,|DC| = 4 cm,

|AD| = 6ñ3 cm.

Find |AB| = x in cm.D

A) 12 B) 6ñ3 + 4 C) 15 D) 16 E) 12ñ3

30° 60°A B

CD

6ñ3

4

x

8. In the figure,

ABCD is a

trapezoid,

[DC] // [AB],

|AE| = |ED|,

[EC] ⊥ [CB],

|DC| = 6 cm,

|EC| = 12 cm, and |AB| = 20 cm.

What is |CB| = x in cm?C

A) 5 B) 8 C) 10 D) 12 E) 13

A B

E

D C6

12x

20


Polygons

20

2. In the figure, ABCDis a trapezoid,

|AD|=|DC|=|BC|,

and m(AéBD) = 40°.

What is m(DéAB) = x in degrees?A

A) 80 B) 75 C) 70 D) 65 E) 60

A B

CD

40°x

3. In the figure,ABCD is atrapezoid,|AD| = |BC|,[CH] ⊥ [AB],AH| = 7 cm,|HB| = 3 cm.

Find |DC| = x in cm.C

A) 6 B) 5 C) 4 D) 3 E) 2

A B

CD

7 3H

x

5. In the figure, ABCDis an isoscelestrapezoid,|AD|=|BC|=8cm

|DC| = 8 cm, and

m(ëB) = 60°.

What is |AB| = x in cm?A

A) 16 B) 15 C) 13 D) 12 E) 10

A B

D C8

8 8

x60°

1. In the figure,ABCD is atrapezoid,[EO] // [AB],|AB| = 8 cm, and|DC| = 4 cm.

Find |EO| = x in cm.B

A B

CD

E

4

8

O

x

4. In the figure,

ABCD is a

trapezoid,

[OP] // [DC] // [AB],

|OP| = 4 cm, and

|DC| = 6 cm.

Find |AB| = x in cm.D

A) 8 B) 9 C) 10 D) 12 E) 16

A B

CD 6

x

4

OP

6. In the figure,ABCD is anisoscelestrapezoid,

m(AéBD) = 40°,

m(AéDB) = 80°.

What is m(DéBC) = x in degrees?C

A) 10 B) 15 C) 20 D) 25 E) 30

A B

CD

80°

40°x


9. In the figure,ABCD is anisoscelestrapezoid,[AC] is anangle bisector,

m(AéCB) = 72°.

What is m(DéCA) = x in degrees?B

A) 48 B) 36 C) 30 D) 24 E) 18

A B

CD

72°x

10. In the figure,ABCD is anisoscelestrapezoid,[DE and [CE]are angle bisector,

and m(CéEF) = 70°.

What is m(DéAB) = x in degrees?A

A) 110 B) 120 C) 130 D) 140 E) 150

A B

CD

70°E

Fx

11. In the figure,ABCD is anisoscelestrapezoid,[DH] ⊥ [AB],|DC| = 6 cm,|HB| = 9 cm.

Find |AH| = x in cm.C

A) 1 B) 2 C) 3 D) 4 E) 5

6

9A B

CD

Hx

12. In the figure,ABCD is anisoscelestrapezoid,[AD] ⊥ [DB],[CH] ⊥ [AB],|AB| = 10 cm,|CH| = 4 cm.

What is |DC| = x in cm?D

A) 3 B) 4 C) 5 D) 6 E) 8

A B

CD

H

4

10

x

8. In the figure,ABCD is anisoscelestrapezoid,[AC] ⊥ [BC],|DC| = 5 cm,|AB| = 13 cm.

Find the height of the trapezoid in cm.D

A) 9 B) 8 C) 7 D) 6 E) 4

A B

CD 5

13

7. In the figure, ABCDis an isoscelestrapezoid,[AC] ⊥ [BD],|AB| = 13 cm,and |DC| = 5 cm.

What is the height of the trapezoid in cm?C

A) 12 B) 10 C) 9 D) 8 E) 6

A B

CD 5

13


Polygons

21

5. In the figure,ABCD is a righttrapezoid,|AB| = 15 cm,|BC| = 15 cm,and |DC|= 6 cm.

Find |AD| = x in cm.E

A) 6 B) 8 C) 9 D) 10 E) 12

A B

CD

15

15

6

x

6. In the figure,ABCD is a righttrapezoid,[AC] ⊥ [CB],|AB| = 20 cm,and |DC|= 2 cm.

What is |AD| = x in cm?C

A) 9 B) 8 C) 6 D) 5 E) 4

A B

CD 2

20

x

1. In the figure,ABCD is a righttrapezoid,|AB| = 10 cm,|AD| = 8 cm, and|DC| = 4 cm.

Find |BC| = x in cm.E

A) 15 B) 13 C) 12 D) 11 E) 10

4

8

10A B

CD

x

3. In the figure,ABCD is a righttrapezoid,[AC] ⊥ [BD],|DC| = 4 cm,|AB| = 9 cm.

What is |AD| = x in cm?D

A) 9 B) 8 C) 7 D) 6 E) 4

4

9A B

CD

x

4. In the figure,

ABCD is a right

trapezoid,

|AD| = 8 cm,

|DC| = 5 cm,

and m(ëA) = 60°.


A) 8 B) 9 C) 10 D) 12 E) 15

A B

CD

60°

8

5

x

2. In the figure,ABCD is aright trapezoid,[AC] is anangle bisector,|BC| = 8 cm,|DC| = 10 cm.

What is |AB| = x in cm?D

A) 12 B) 14 C) 15 D) 16 E) 18

A B

CD 10

8

x


11. ABCD is a righttrapezoid,|AE| = |ED|,

|BH| = |HC|,

[HF] ⊥ [AB],

|EF| = 17 cm,

|HF| = 8 cm,|DC| = 10 cm.

What is |AB| in cm?A

A) 20 B) 22 C) 24 D) 25 E) 30

A B

CD 10

HE

817

F

9. In the figure,ABCD is anisoscelestrapezoid,[BE] is ananglebisector,

[AE] ⊥ [EB], and A, D and E are collinear points.

What is m(AéDC) = x in degrees?E

A) 150 B) 140 C) 135 D) 130 E) 120

A B

CD

E

x

12. In the figure,ABCD is anisoscelestrapezoid,|AB| = 15 cm,|AD| = 7 cm,|BC| = 7 cm,|DC| = 8 cm.

Find |BD| = x in cm.B

A) 14 B) 13 C) 12 D) 10 E) 9

8

15A B

CD

x7 7

8. In the figure, ABCD isa right trapezoid,[DC] // [AB],[CE] and [BE] areangle bisectors,|DC| = 6 cm,|AB| = 8 cm, and|BC| = 10 cm.

Find |EF| = x in cm.C

A B

CD

F E

8

10

6

x

10. In the figure,ABCD is a righttrapezoid,[DC] // [AB],|DC| = 4 cm,|DB| = 15 cm,and |AD| = 9 cm.

What is |CB| = x in cm?D

A) 11ñ2 B) ó130 C) 13ñ2

D) ó145 E) 5ò14

x

A B

CD 4

915

7. In the figure,ABCD is a righttrapezoid,|AB| = |AD|, and

m(BéDC) = 65°.

What is m(DéAB) = x in degrees?B

A) 40 B) 50 C) 55 D) 60 E) 65

65°

A B

CD

x


Polygons

224. In the figure,

[AB] // [KN] // [DC],

|DK| = 6 cm,

|DC| = 8 cm,

|KN| = 12 cm, and

|AB| = 14 cm.

What is |AK| = x in cm?A

8

6

x

14

12

A B

CD

K N

3. In the figure,ABCD is atrapezoid,[EF] // [CB],|EF| = 4 cm,|CB| = 10 cm,|EA| = 6 cm.

Find |ED| = x in cm.C

A) 6 B) 8 C) 9 D) 10 E) 12

D

A B

C

6 4

F

E 10

x

1. ABCD is atrapezoid,[AE] and [DE]angle bisectors,[EF] // [AB] // [DC]|AD| = 10 cm,|DC| = 9 cm,|AB| = 13 cm.

What is |EF| = x in cm?B

A B

CD

EF10

9

13

x

5. In the figure,ABCD is a righttrapezoid,[BE] ⊥ [AD],|AB| = 15 cm,|BC| = 12 cm,and |DC|= 6 cm.

Find |BE| = x in cm.A

A) 12 B) 10 C) 9 D) 8 E) 6

x

6

12

15

E

A B

D C

6. In the figure,ABCD is a

trapezoid,

[DH] ⊥ [AB],

|AB| = 15 cm,

|BC| = 6 cm,

|DC| = 5 cm, and |AD| = 8 cm.

What is |DH| = x in cm?E

A) 3 B) 3,6 C) 4 D) 4,2 E) 4,8

D

A B

C5

68

H

x

2. In the figure,ABCD is atrapezoid,[AD] ⊥ [DB],|AD| = |DB|,|AB| = 24 cm,|DC| = 7 cm.

What is |BC| = x in cm?D

A) 9 B) 10 C) 12 D) 13 E) 15

D 7

24A B

C

x


11. ABCD is atrapezoid,

[EC] ⊥ [BC],

|AE| = |ED|,

|DC| = 6 cm,

|EC| = 8 cm,|AB| = 14 cm.

Find |BC| = x in cm.D

A) 8 B) 9 C) 10 D) 12 E) 14

6

8

A B

CD

14

E x

10. In the figure,ABCD is a trapezoid,|DE| = |DC|,|AB| = |AE|,

m(EéBC) = θ,

m(EéCB) = α, andα – θ = 20°.

What is θθ in degrees?C

A) 55 B) 45 C) 35 D) 30 E) 25

A B

CD

E

q

a

9. In the figure,ABCD is a righttrapezoid, EAB is an equilateral triangle,

|AB| = 4ñ3 cm, |AD| = x, and|BC| = y.

Find the value of the sum x + y in cm.D

A) 6 B) 8 C) 9 D) 12 E) 18

x

y

E

D

A B

C

4ñ3

12. In the figureABCD is a righttrapezoid, |AB| = |AD|,

|BC| = 3ñ3 cm,

|DC| = 3 cm.

What is measure of the angle ADC in degrees?D

A) 150 B) 140 C) 130 D) 120 E) 105

3

A B

CD

3ñ3

7. In the figure,ABCD is a righttrapezoid,

|DE| = |EC|,

|AB| = 10 cm,

|EB| = 13 cm,

|AD| = c, and

|BC| = a.

Find the value of the sum a + c in cm.E

A) 12 B) 16 C) 18 D) 20 E) 24

A B

C

D

E

13

c

a

10

8. In the figure,ABCD is a righttrapezoid, [AH] ⊥ [BD],|AB| = 20 cm,|BC| = 12 cm,and |DC| = 9 cm.

What is |AH| = x in cm?B

A) 18 B) 16 C) 15 D) 12 E) 10

9

12

20A B

D C

H

x


Polygons

234. In the figure,

ABCD is atrapezoid,[DE] ⊥ [BC],[AD] ⊥ [AE],[DE] is anangle bisector,

|AE| = 12 cm, and |DE| = 20 cm.


A) 12 B) 13 C) 15 D) 18 E) 20

A B

CD

E

20

12

x

5. In the figure,ABCD is a righttrapezoid, [HB] ⊥ [AD], |AB| = 17 cm,|AH| = 8 cm, and|HD| = 9 cm.

What is |DC| = x in cm?D

A) 5 B) 6 C) 8 D) 9 E) 10

8

9

H

A B

CD

17

x

3. In the figure,ABCD is atrapezoid, |AE| = |ED|,|DC| = 6 cm,|AB| = 9 cm, and|FB| = 6 cm.

What is |EF| = x in cm?C

6

6F

9A B

CD

E x

1. In the figure, |AE| = |ED|,

|EG| = |GF|,

[DG] is an anglebisector,

|DC| = 12 cm,

|AB| = 16 cm,

and [DC] // [EF] // [AB].

What is |AD| in cm?E

A) 28 B) 24 C) 20 D) 16 E) 14

A B

CD

G

12

16

E F

2. ABCD is atrapezoid,[CE] and [DF]are anglebisectors,|AD| = 7 cm,|BC| = 9 cm, |EF| = 2 cm.

Find the value of the ratio D

A B

CD

E F2

7 9

6. In the figure,ABCD is atrapezoid, |AB| = a,

|AD| = d,

|DC| = c, and

m(ëB) = 55°.

If a = c + d then, what is the measure of theangle ADC in degrees?

BA) 100 B) 110 C) 115 D) 120 E) 125

c

d

a55°

D

A B

C


ABCD is a trapezoid, [EC] ⊥ [CB],

[CH] ⊥ [AB],

|AE| = 2⋅|DE|,

|BC| = 5 cm,

|EC| = 4 cm.

What is |CH| = x in cm?E

E

A B

CD

x 5

4

H

11.

In the figure, ABCD is a trapezoid, |AE| = 20 cm,|EB| = 17 cm, |BC| = 30 cm, |AD| = 16 cm, and |DC| = 3 cm.

Find |CE| = x in cm.A

A B

CD

E

16

20 17

30

3

x

7. In the figure,ABCD is a righttrapezoid, [AE] and [BE] areangle bisectors, |AE| = 15 cm,and |BE| = 20 cm.

What is |DC| = x in cm?E

A) 12 B) 15 C) 18 D) 20 E) 24

A

B

CD

E

15

20

x

8. In the figure,ABCD is atrapezoid,[DC] // [AB],[CE] // [AD],|DC| = 9 cm,|AB| = 15 cm,|EB| = 4 cm.

Find |DE| = x in cm.C

A) 4 B) 5 C) 6 D) 8 E) 9

A B

CD

E 4

15

9

x

9. In the figure,ABCD is atrapezoid,[BE] ⊥ [AD],[CH] ⊥ [AB],

m(ëA) = 75°.

What is value of the ratio ?D

A B

CD

H

75°

E

12. In the figure, ABCD is a trapezoid,[AN], [BK], [CK] and[DN] are anglebisectors, |AB| = 12 cm,|DC| = 4 cm,|BC| = 10 cm, and|AD| = 8 cm.

What is |KN| in cm?B

A B

CD

EK N

F

4

12

Kites Assignment Test

Polygons

24

2. In the figure,ABCD is a kite,

m(CéBE) = 77°,

and

Find the measure of the angle DCB in degrees.C

A) 22 B) 34 C) 44 D) 60 E) 72

A

D

C

B 77°

E


|AB| = |AD|,

m(AéCD) = 26°,

m(BéAC) = 48°,

m(AéDB) = x, and

m(CéBD) = y.

What is value of the difference y – x in degrees?B

A) 18 B) 22 C) 26 D) 30 E) 32

C

A

B D

48°

26°

yx

1. In the figure,ABCD is akite,

m(ëA) = 40°,

m(ëC) = 70°.

What is measure of the angle ABC in degrees?A

A) 125 B) 120 C) 115 D) 110 E) 105

A

D

C

B

40° 70°

3. In the figure,ABCD is akite,|AB| = 9 cm,|BD| = 6 cm,

m(ëC) = 60°.

What is the perimeter of the kite in cm?C

A) 18 B) 24 C) 30 D) 36 E) 48

9

6 60°A

B

C

D

6. In the figure,ABCD is akite,

|AE| = |ED|,

|BF| = |FC|,

|EO| = 5 cm,

|OF| = 3 cm.

Find the perimeter of the kite in cm.C

A) 16 B) 24 C) 32 D) 36 E) 40

A

D

C

B

5

3

O

E

F


|AB| = 6 cm,

|DC| = 9 cm.

What is the value of |EC|2 – |AE|2?D

A) 81 B) 64 C) 54 D) 45 E) 36

EA

B

C

D

9

6


ABCD is a kite,

m(ëA) = 60°,

m(ëC) = 120°,

|AB| = |AD| = x,

|BC| = |DC| = y.

What is the value of the ratio ?A

A

B

C

D

x y

x y

60° 120°


|AB| = |BC|,

m(ëB) = 40°, and

m(ëC) = 110°.

Find m(AéDC) = x in degrees.B

A) 90 B) 100 C) 110 D) 120 E) 130

110°

40°

A C

D

B

x


[AB] ⊥ [AD],

m(ëB) = 105°, and

|AD| = 4 cm.

What is |CD| = x in cm?D

A) 4 B) 5 C) 2ñ7 D) 4ñ2 E) 6

105°

4

x

A

B D

C


m(BéDC) = 60°,|CD| = 12 cm,

and |DA| = 3ñ7 cm.

What is |AC| in cm?B

A) 6ñ3 B) 9ñ3 C) 10ñ3 D) 12ñ3 E) 18

C

A

B D60°

E

12

3ñ7

9. In the figure,ABCD is a kite,|BC| = |CD|,

m(CéAD) = 30°,|BE| = 3 cm.

What is |AD| = x in cm?E

A) 3 B) 4 C) 5 D) 3ñ3 E) 6

A

B D

C

E3

x

30°

8. In the figure,ABCD is a kite,|AB| = |AD|,[AE] and [DE]are anglebisectors,

m(A éED) = 70°,

m(BéCD) = 40°.

Find m(AéBC) = x in degrees.C

A) 80 B) 90 C) 100 D) 110 E) 120

A

DB

C

E

70°x

40°

Kites Assignment Test

Polygons

25

6. ABCD is a kite,

|AB| = |BC|,

|AE| = 6 cm,

|ED| = 9 cm,

|CD| = 5 cm.

What is |AB| = x in cm?C

A) 8 B) 9 C) 10 D) 12 E) 15

A

B C D

E

6

9x

5

3. ABCD is akite,|AD| = |AB|,

[PE] ⊥ [AB],

[PF] ⊥ [BC],

[PK] ⊥ [CD|,

[PL] ⊥ [DA].

What is the value of the ratio ?B

PA

B

C

DL

E

K

F

4.

In the figure, ABCD is a kite, |AB| = |AD|,

m(BéAC) = m(EéDC), |EC| = 8 cm, |BC| = 12 cm.

What is |AE| = x in cm?E

A) 18 B) 16 C) 13 D) 12 E) 10

A

B

D

EC

8

12

x


|AB| = |BC|,

|AB| = 9 cm,

|DC| = 8 cm, and

|EB| = 7 cm.

Find the measure of the angle BDA in degrees.C

A) 60 B) 50 C) 45 D) 40 E) 30

A C

D

B

79

8

E

2.

In the figure, ABCD is a kite, |DE| = 10 cm,|AB| = |BC| = 8 cm, and |AD| = |DC| = 5 cm.

Find |CE| = x in cm.AA) 8 B) 9 C) 10 D) 11 E) 12

A

B C

D

Ex

8

8

5

510


[DA] ⊥ [AB]

|AD| = 5ñ2 cm,

|AB| = 5ñ2 cm,

|DC| = 13 cm,

|BC| = 13 cm.


A) 12 B) 14 C) 15 D) 17 E) 20

5ñ2 13

A

B

C

D

5ñ2 13


8. In the figure,ABCD is a kite,BCE is anequilateraltriangle,

m(ëA) = 70°,

m(AéBE) = 40°.

What is m(AéDE) = x in degrees?D

A) 10 B) 15 C) 20 D) 25 E) 30

E

40°

70°A

B

C

D

x

7. ABCD is a kite,|BF| = |FC|,|DE| = |EC|,

m(ëA) = 50°,|DE| = 2 cm,|BF| = 2 cm,

|EF| = 2ñ3 cm.

Find the measure of the angle ABC in degrees.A

A) 95 B) 100 C) 105 D) 110 E) 115

2

D

E

C

F2

B

A 50° 2ñ3


|AB| = |AD|,

[CE] is an angle

bisector,

m(AéBE) = m(EéBC),

m(BéAD) = 110°,

m(BéEC) = 110°.

Find m(BéCD) in degrees.B

A) 25 B) 30 C) 35 D) 40 E) 45

A

B D

C

E

110°

110°


|AB| = |AD| = |BE|

[BE] is an angle

bisector,

m(DéAF) = 10°,

m(BéCD) = 50°,

m(BéEA) = x.

What is m(BééEA) = x in degrees?D

A) 45 B) 50 C) 55 D) 60 E) 75

A

B D

C

E

10°

50°

x

F


[AC] is diagonal,

|AD| = |AB|,

3|CF| = 2|FB|,

and |EF| = 4 cm.

Find |DE| = x in cm.E

A) 6 B) 7 C) 8 D) 9 E) 10

A B

C

D

E

4

x

F


|AB| = |AD|,

[AB] ⊥ [AD],

|CD| = ò10 cm,

and |AC| = 4 cm.


A) 1 B) ñ2 C) 2 D) 2ñ2 E) 3

C

A

B DE

x

ò10

Test - 1

1. A2. C3. A4. C

5. B6. C7. B8. E

9. A10. D11. D12. B

13. B14. B15. E16. B

Test - 2

1. B2. D3. C

4. C5. C6. A

7. D8. A9. C

10. D11. E12. D

Introduction to Polygons

Test - 3

1. C2. A3. A

4. D5. D6. D

7. C8. E9. D

10. A11. B12. A

Test - 4

1. D2. D3. A

4. E5. B6. C

7. D8. A9. B

10. B11. C12. B

Test - 5

1. B2. E3. D

4. A5. E6. E

7. D8. C9. C

10. A11. C12. B

Quadrilaterals

Test - 6

1. C2. D3. B

4. A5. E6. E

7. C8. D9. B

10. A11. A12. B

Test - 7

1. B2. C3. D

4. A5. B6. C

7. D8. B9. A

10. B11. C12. B

Test - 8

1. C2. C3. C

4. D5. E6. C

7. A8. C9. C

10. C11. B12. A

Test - 9

1. D2. A3. C

4. D5. C6. E

7. B8. D9. C

10. D11. B12. C

Parallelogram

Test - 10

1. A2. D3. C

4. B5. E6. C

7. A8. E9. B

10. B11. C12. B

Test - 11

1. D2. C3. C

4. D5. D6. E

7. D8. E9. B

10. C11. D12. E

Test - 12

1. A2. B3. D

4. C5. C6. B

7. E8. B9. E

10. B11. E12. C

Rectangle

POLYGONS

Test - 13

1. E2. B3. C

4. D5. A6. C

7. A8. B9. D

10. C11. C12. E

Test - 14

1. C2. B3. D

4. E5. E6. A

7. D8. C9. D

10. D11. A12. B

Rhombus

Test - 15

1. C2. B3. D

4. B5. D6. E

7. A8. E9. A

10. C11. D12. C

Test - 16

1. D2. B3. B

4. C5. B6. D

7. A8. A9. B

10. D11. E12. D

Test - 17

1. A2. A3. B

4. D5. D6. C

7. C8. D9. D

10. D11. E12. E

Test - 18

1. A2. E3. D

4. A5. C6. C

7. D8. C9. B

10. E11. B12. D

Square

Test - 19

1. B2. D3. B

4. E5. A6. A

7. D8. C9. C

10. E11. D12. C

Test - 20

1. B2. A3. C

4. D5. A6. C

7. C8. D9. B

10. A11. C12. D

Test - 21

1. E2. D3. D

4. B5. E6. C

7. B8. C9. E

10. D11. A12. B

Test - 22

1. B2. D3. C

4. A5. A6. E

7. E8. B9. D

10. C11. D12. D

Test - 23

1. E2. D3. C

4. C5. D6. B

7. E8. C9. D

10. E11. A12. B

Trapezoid

Test - 24

1. A2. C3. C

4. B5. D6. C

7. B8. C9. E

10. A11. B12. D

Test - 25

1. D2. A3. B

4. E5. C6. C

7. A8. D9. B

10. B11. E12. D

Kite

polygons - wordpress.com of one interior angle of a convex polyon? e a)108 b)120 c)135 d)140 e)145...

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