geometry module 1 assessments

Geometry

Module 1 Assessments

Student Edition

G8_FM_SE.indd 1 6/3/21 9:34 PM

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USING A RECTANGULAR COORDINATE SYSTEM: Standardized Test • 1

USING A RECTANGULAR COORDINATE SYSTEM

End of Topic AssessmentName Date

1. Right triangle DEF has vertices at D (0, 0) and E (10, 0). Which best describes possible locations of point F?

a. Any point on the line y = 10 except where x = 0

b. Any point on the line y = 0 except where x = 10

c. Any point on the line x = 10 except where y = 0

d. Any point between D and E except where y = 0

2. Quadrilateral DEFT has vertices D (2, 7), E (–4, 4), F (5, –6), and T (11, –3). What is the best name for quadrilateral DEFT?

a. trapezoid

b. square

c. parallelogram

d. rectangle

3. Square MNPR has points M (3, 8) and N (–2, –4). What is the slope of line segment NP?

a. − 5 _ 12

b. 12 _ 5

c. 5 _ 12

d. The slope cannot be determined.

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2 • MODULE 1: REASONING WITH SHAPES


4. What is the first step in constructing the perpendicular bisector of line segment AB?

A B

a. Place the point of the compass at point B and draw an arc between points A and B.

b. Place the point of the compass at point A and draw an arc between points A and B.

c. Place the point of the compass at point B and open the compass so that it is greater than half of the distance from point B to point A.

d. Use your straightedge to draw a line through the intersections of the arcs.

5. Square ABCD has points A (5, 10) and B (–4, 3). What is the slope of line segment BC?

a. 9 _ 7

b. 7 _ 9

c. − 9 _ 7

d. − 7 _ 9

6. Which is the slope of a line that is perpendicular to the line that passes through the points (–9, –4) and (3, 4)?

a. − 3 _ 2

b. − 2 _ 3

c. 2 _ 3

d. 3 _ 2

7. Regular polygon ABCDE is graphed on the coordinate plane. The polygon has points C (3, 7) and D (3, –1). What is the perimeter of ABCDE?

a. 28 units

b. 32 units

c. 40 units

d. 48 units

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8. A triangle on the coordinate plane has points located at A (2, 5), B (5, 9), and C (8, 5). What is the area of the triangle?

a. 8 square units

b. 10 square units

c. 12 square units

d. 24 square units

9. Square PINT has vertices N (4, 2) and T (3, 8). What is the area of square PINT?

a. 6.08 square units

b. 24.33 square units

c. 37 square units

d. 49 square units

10. Consider the graphed equation below. What is the equation of the line that passes through (–3, 2) and is parallel to the graphed equation?

−4−2

20 4

−4

4

2

y

x−2

a. y = x – 1

b. y = –x – 1

c. y = –x + 4

d. y = –x + 2

11. What is the area of quadrilateral WXYZ?

−2−4−6−8 20

2

−2

−4

−6

−8

4

6

8

4 6 8 x

y

XW

YZ

a. 40.88 square units


c. 100 square units

d. 109 square units

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12. What is the area of the composite figure?

−6−12−18−24 60

6

−6

−12

−18

−24

12

18

24

12 18 24 x

y

a. 125 square units


c. 810 square units

d. 1080 square units

13. Which statement is true?

−2−4−6−8 20

2

−2

−4

−6

−8

4

6

8

4 6 8 x

y

L

M

N

a. Triangle LMN is a right isosceles triangle.

b. Triangle LMN is an acute isosceles triangle.

c. Triangle LMN is an equilateral triangle.

d. Triangle LMN is a right scalene triangle.

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14. Which is closest to the perimeter of the figure shown on the graph?

−6−12−18−24 60

6

−6

−12

−18

−24

12

18

24

12 18 24 x

y

a. 110 units

b. 130.6 units

c. 126 units

d. 64.6 units

15. Jonas constructed a segment bisector as shown. What is NOT true about the segment bisector?

A B

a. It is perpendicular to line segment AB.

b. It divides line segment AB into two congruent line segments.

c. It is exactly the same length as line segment AB.

d. The distance from A to any point on the bisector is equal to the distance from B to the same point on the bisector.

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RIGID MOTIONS ON A PLANE: Standardized Test • 1

RIGID MOTIONS ON A PLANE


1. Which shows a line of reflection between the two figures?

a. b.

c. d.

2. What is the rotational symmetry of the figure?

a. 45°

b. 90°

c. 270°

d. The figure has no rotational symmetry.

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2 • MODULE 1: Reasoning with Shapes


3. Which of these figures has no lines of symmetry?

a. b.

c. d.

4. Which point is the center of the rotation for the figures shown?

A

B

C

D

a. A

b. B

c. C

d. D

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5. Which diagram shows the reflection R n (H) = H ′ ?

a.

H

H'

n

b.

H H'

n

c.

H

H'

n

d.

H

H' n

6. Which figure shows line v as a perpendicular bisector of ‾ NZ ?

a.

N

Z

v

b.

Z

N

v

c.

Z

N

v

d.

Z

N

v

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7. Which is the best description of congruent line segments?

a. line segments that are parallel

b. perpendicular line segments

c. line segments that have the same length

d. line segments that share a vertex

8. Which diagram shows the rotation R C,−90 (ABCD) = A ′ B ′ C ′ D ′ ?

a.

C

A’

AB’ C’

D’

B

CD

b.

C

A

A’B’

C’ D’B

CD

c.

C

B’

A

C’D’

A’

B

CD

d.

C

A’A

B’C’

D’B

CD

© C




9. Which sequence of transformations will carry the given pre-image onto the image shown with dashed lines?

A

B B′

A′

C

a. rotate 180° about C , then reflect across B′C′

b. reflect across a vertical line through C

c. both a and b are correct

d. neither a nor b are correct


A

D C C′ D′

BB′ A′

a. reflect across a horizontal line through B , then translate to the left

b. reflect across a horizontal line through the center of ABCD , then translate to the right

c. rotate 180° about B , then translate to the left

d. rotate 90º about D, then reflect across line segment AB

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11. Which shows the correct translation, given the function T M A ′ (octagon)?

a. b.

c. d.

© C




12. Which shows the correct reflection, given the function R n (ABC)?

a. b.

c. d.

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13. Which describes the coordinates of point (x, y) after a 270° counterclockwise rotation about the origin?

a. (–y, x)

b. (–x, –y)

c. (y, –x)

d. (x, y)

14. How many lines of symmetry does a regular pentagon have?

a. 0

b. 3

c. 4

d. 5

15. Which rotational angle measure is NOT a rotational symmetry of the equilateral triangle shown?

a. 30º

b. 60º

c. 120º

d. 180º

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16. The diagram below shows the arcs and segments used to construct ∆ ABC , given line k.

kW

C

BA

Based on the construction, which statement is true?

a. ‾ AW ≅ ‾ BW

b. ‾ AW ≅ ‾ CW

c. ‾ CW ≅ ‾ BW

d. ‾ AC ≅ ‾ CW

17. Which algebraic representation indicates reflecting a shape over the x-axis, translating the shape up 2 units and right 5 units on the coordinate plane?

a. (x + 5, –y + 2)

b. (x – 5, –y + 2)

c. (–x + 5, y + 2)

d. (–x – 5, y + 2)

© C




Mid-Topic AssessmentName Date

1. Which diagram shows the translation T GH (X) = X ′ ?

a.

H X

X'G

b.

H X

X'

G

c.

H X

X'

G

d.

H XX'

G

2. Which diagram shows an isometry?

a.

B

B'

C'

A

A'

C

b.

B'B

C'A

A'

C

c.

A

A' D'

B' C'

B C

D

d.

A

B

C

A'

B' C'

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3. Which sequence of transformations will NOT carry the given pre-image onto the image shown with dashed lines?

A'

AB

C

C'

B'

a. rotate−90°aboutpointC , then translate the distance CC′

b. reflectacross̄ AC , then translate up

c. translate the distance CC′ , then rotate −90°aboutC .

d. translate the distance AA′ , then rotate −90°aboutA


BA

DC

C′ A′

D′ B′

a. reflectacross‾ BD ,thenrotate−270°

b. rotate−90°aboutD , then translate to the right

c. translatetotheright,thenrotate90°aboutA

d. rotate90°aboutD,thenreflectacross ‾ AB

© C




5. ∆ ABC and∆ PQR are shown in the diagrambelow.

50° 60°C

B

A

R

Q

P

Based on the information provided in the diagram, which statement is true?

a. ‾ AB ≅ ‾ RP

b. ‾ AB ≅ ‾ PQ

c. ‾ RP ≅ ‾ BC

d. ‾ PQ ≅ ‾ AC

6. ∆ ABC and∆ PQR are shown in the diagrambelow.

50° 60°C

B

A

R

Q

P

Based on the information provided in the diagram, what is the measure of angle Q?

a. 50º

b. 60º

c. 70º

d. 110º

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7. Triangle DEF is transformed to form triangle D′E′F ′.

0

–4

–6

–8

–2–3

–5

–7

–1

2

4

6

8

1

3

5

7

2 x

y

41 3 6 8 9 10 11 125

E

E9

F9

FD

D9

7

Whichruledescribesthetransformationthat was used to form triangle D′E′F′?

a. (y, –x)

b. (y, x)

c. (x, –y)

d. (–x, y)

8. Quadrilateral ABCD is transformed to form quadrilateral A′B′C ′D′.

0

–4

–6

–8

–2–3

–5

–7

–1

2

4

6

8

1

3

5

7

2 x

y

41 3 6 8 9 10 11 125

A

BB9

C C9

D

7

A9

D9

Whichruledescribesthetransformationthat was used to form quadrilateral A′B′C′D′?

a. (y + 2, x)

b. (y, x + 2)

c. (x + 2, –y)

d. (x + 2, y)

© C




9. Which sequence of isometries shows thatthetwofiguresarecongruent?

a. rotate180ºandtranslateright

b. rotate90ºcounterclockwise

c. rotate90ºclockwise

d. rotate180ºandtranslateleft

10. Which rotational angle measure is not a rotational symmetry of the regular hexagon shown?

a. 60º

b. 120º

c. 240º

d. 330º

© C


CONGRUENCE THROUGH TRANSFORMATIONS: Standardized Test • 1

CONGRUENCE THROUGH TRANSFORMATIONS


1. Consider the following statement:Clothes that are expensive are made of better materials.

Which is the hypothesis of the statement?

a. Clothes are expensive.

b. Clothes are made of better material.

c. Clothes are not expensive.

d. Clothes last longer.

2. For which drawing can you use the given information and the SSS Congruence Theorem to prove that the triangles are congruent?

a. b.

c. d.

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3. The image in this figure was formed by reflecting ΔLXP over the x -axis. What is a congruence statement that describes these triangles?

D

W

T

L

P

X

a. ∠X ≅ ∠W

b. ∠L ≅ ∠D

c. ∠W ≅ ∠P

d. ∠T ≅ ∠X

© C




4. If the truth value of a conditional statement is false, what are the truth values of p and q ?

a. p is true and q is true

b. p is true and q is false

c. p is false and q is true

d. p is false and q is false

5. Which set of congruence statements shows that ΔPSC ≅ ΔRGM by the SAS Triangle Congruence Theorem?

M

R

GS

C

P

a. ‾ PS ≅ ‾ RG

‾ PC ≅ ‾ RM

∠SPC ≅ ∠GRM

b. ‾ PS ≅ ‾ RG

‾ SC ≅ ‾ GM

∠SCP ≅ ∠GMR

c. ‾ PC ≅ ‾ RM

‾ CS ≅ ‾ MG

∠SPC ≅ ∠GRM

d. ‾ PC ≅ ‾ RM

‾ PS ≅ ‾ RG

∠PCS ≅ ∠RM

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6. Which states the following?“If point B is on ‾ AC and between points A and C , then AB + BC = AC .”

a. Segment Addition Postulate

b. Addition Property

c. Congruent Supplement Theorem

d. definition of a midpoint

7. Which set of congruence statements shows that ΔRTS ≅ ΔVXW by the SSS Triangle Congruence Theorem?

V

W

T

S

R

X

a. ‾ TR ≅ ‾ XV

‾ ST ≅ ‾ WV

‾ RS ≅ ‾ XW

b. ‾ RT ≅ ‾ VW

‾ RS ≅ ‾ VX

‾ ST ≅ ‾ WX

c. ‾ RT ≅ ‾ VX

‾ TS ≅ ‾ XW

‾ SR ≅ ‾ WV

d. ‾ TR ≅ ‾ WX

‾ RS ≅ ‾ VW

‾ ST ≅ ‾ XV

© C




8. In the figure shown, ΔABD and ΔDBC are isosceles triangles with bases ‾ AD and ‾ DC and ∠ABD ≅ ∠CBD . Which theorem can be used to prove ΔABD ≅ ΔCBD ?

B

AD

C

a. SSS

b. SAS

c. SSA

d. AAA

9. In ΔCAN , Q is the midpoint of ‾ AC , and V is the midpoint of ‾ AN . What information is needed to prove ΔCQH ≅ ΔNVH ?

N

V

A

Q

CH

a. ∠AQH ≅ ∠AVH

b. ‾ QH ≅ ‾ VH and ‾ CH ≅ ‾ NH

c. ‾ QH ≅ ‾ VH and ∠QHC ≅ ∠VHN

d. ∠HCN ≅ ∠HNC and ∠QHC ≅ ∠VHN

10. Triangle BUN is isosceles with ‾ BU ≅ ‾ BN . What additional given information is needed to prove ΔBUG ≅ ΔBNA by ASA ?

B

NAGU

a. ∠UBA ≅ ∠NBG

b. ∠UBG ≅ ∠NBA

c. ∠BGU ≅ ∠BAN

d. ∠BUG ≅ ∠BNA

11. Triangle BAG is isosceles with ‾ BG ≅ ‾ BA . What is one additional piece of information that is needed to prove ΔBGN ≅ ΔBAU by SAS ?

B

NAGU

a. ‾ GN ≅ ‾ AU

b. ‾ BU ≅ ‾ BN

c. ‾ AU ≅ ‾ AN

d. ‾ AG ≅ ‾ GA

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12. Which congruence theorem best expresses the relationship showing that the triangles below are congruent?

64°

64°

72°

72°

a. SSS

b. SSA

c. SAS

d. ASA

13. Based on the diagram, which congruence statement is true?A

B C

D

E

a. ‾ AC ≅ ‾ DE

b. ‾ BC ≅ ‾ EC

c. ∠C ≅ ∠D

d. ∠ACB ≅ ∠DCE

© C




14. Which congruence statements can be used to show ΔKLM ≅ ΔRST ?S

R

T

L

M

K

a. ‾ KM ≅ ‾ RT and ‾ LK ≅ ‾ SR

b. ‾ KM ≅ ‾ RT and ‾ KM ≅ ‾ ST

c. ∠K ≅ ∠R and ‾ KM ≅ ‾ RT

d. ∠K ≅ ∠R and ∠L ≅ ∠S

15. What measures do you need to prove two triangles congruent?

a. two sides and the included angle

b. three angles

c. two sides

d. a corresponding angle and a corresponding side

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16. What information is NOT needed to prove congruence of ΔRSW and ΔTUV by the SAS congruence theorem?

R W

S

T V

U

a. ‾ SR ≅ ‾ UT

b. ‾ VU ≅ ‾ WS

c. ‾ RW ≅ ‾ TV

d. ∠R ≅ ∠T

17. Consider the conditional statement. If I do my chores, then I get my allowance.

Which statement is true?

a. The conclusion is “I get my allowance.”

b. The hypothesis and the conclusion cannot both be true.

c. If the hypothesis is false then the statement must be false.

d. If the hypothesis is true and the conclusion is false, then the statement is true.

© C




18. The image in this figure was formed by reflecting ΔGHK over the y -axis and then over the x -axis. Which congruence statement is NOT true?

20–2–2

2

4

6

8

y

K

HG

NM

Px

–4

–6

–8

–4–6–8 4 6 8

a. ‾ GH ≅ ‾ MN

b. ‾ KH ≅ ‾ PN

c. ∠K ≅ ∠N

d. ∠G ≅ ∠M

19. A statement is given below. If a four-sided shape has two sides the same length, then it must be a rectangle. Which shape does NOT provide a counterexample to the statement?

a. rhombus

b. square

c. trapezoid

d. kite

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20. Which of the following statements is false?

a. A postulate is a statement that can be proven.

b. The essential difference between Euclidian geometry and non-Euclidian geometry is the nature of parallel lines

c. The transitive property states that “if a = b and b = c, then a = c.”

d. All right angles are congruent.

21. For the triangle shown, what could you use to prove that AD + DB = AB?

DE

A

C B

a. definition of a midpoint

b. definition of congruent segments

c. Segment Addition Postulate

d. Linear Pair Postulate

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