chapter 7 practice test #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/...chapter 7...

Chapter 7 Practice Test #1

Class Name : M29 Geometry - 2019-20 Term 2 Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. Draw the image of the following segment after a dilation centered at the origin with a scale factor of .

2. A dilation centered at the origin with a scale factor of is applied to

23

3

xx

2 4 6 8 10 12 14 16 18

yy

2

4

6

8

10

12

14

16

18

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 7 Pr ac t i ce T es t #1 / 19

2. A dilation centered at the origin with a scale factor of is applied to .

The result is , as shown below.

(a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in theblanks to give the coordinates after the dilation.

original coordinates final coordinates

_____, _____

_____, _____

_____, _____

(b) Choose the general rule below that describes the dilation mapping to .

3. For the figure below, do a dilation centered at the origin with a scale factor of

3 XYZ

X 'Y 'Z '

→X , −1 4 → X 'Y , 3 2 → Y '

Z , −3 −1 → Z '

XYZ X 'Y 'Z '

, x y → , 3y 3x , x y → , 3x y

, x y → , x 3y , x y → , 13 x

13 y

, x y → , 13 y

13 x , x y → ,

13 x 3y

, x y → , 3x 3y , x y → , 3x13 y

3

xx

-2-4-6-8-10-12 2 4 6 8 10 12

yy

-2

-4

-6

-8

-10

-12

2

4

6

8

10

12

X

Y

Z

X '

Y '

Z '


3. For the figure below, do a dilation centered at the origin with a scale factor of .

Then, give the endpoints for both the original figure and the final figure.

Endpoints of original figure:

Left: ____ ____ Right: ____ ____

Endpoints of final figure:

Left: ____ ____ Right: ____ ____

4. Which pairs of figures are congruent? Which pairs are similar?

3

Dilation

, ,

, ,

xx

2 4 6 8 10 12 14 16 18 20

yy

2

4

6

8

10

12

14

16

18

20

0


4. Which pairs of figures are congruent? Which pairs are similar?

5. The quadrilaterals and are similar.

Find the length of .

6. The table below gives the dimensions of a sculpture and a scale model of the sculpture.

Congruent? Yes No Congruent? Yes No

Similar? Yes No Similar? Yes No



JKLM PQRS

x SP

L

2

4

3

7K J

MR

2.8

5.6

x

9.8Q P

S


6. The table below gives the dimensions of a sculpture and a scale model of the sculpture.

Find the scale factor of the model to the real sculpture. Write your answer as a fraction in simplest form.

Sculpture Model

Length (inches)

Width (inches)

Height (inches)

7.

(The triangles are not drawn to scale.)

8. The two triangles below are similar.

49 7

35 5

56 8

A

B

C D

E

F

45 ?

63 7

5 8

and are similar. Find the missing side length.ΔABC ΔDEF


8. The two triangles below are similar.

Also, and as shown below.

Find , , and .

Assume the triangles are accurately drawn.

____

____

____

9. In a scale model of a table, centimeter represents inches.

=m∠ F 60 ° =m∠ E 95 °m∠ J m∠ K m∠ L

m∠ J = °m∠ K = °m∠ L = °

1 9

G

FE

60° 95°

K

J

L


9. In a scale model of a table, centimeter represents inches.

Scale

Answer the following.

(a) The height of the real table is inches. What is the height ofthe table in the scale model?

____ centimeters

(b) In the scale model, the length of the table is centimeters.What is the length of the real table?

____ inches

10. Find the length .

11. A pole that is tall casts a shadow that is long. At the same time, a nearby building casts a

shadow that is long. How tall is the building? Round your answer to the nearest meter.

12. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifying

1 9

:1 cm 9 in

18

4

x

3.3 m 1.08 m48.25 m

2

x

3

7.5


12. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifyingthe similarity.

If necessary, you may learn what the markings on a figure indicate.

Not similar or not necessarily similar

Similar: ___, by the

Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property

Side-Angle-Side (SAS) Similarity Property









13. Use the given information to prove that .

Given:

Prove:

14. In the figure below, and are perpendicular.

STU ~

JKL ~

ABC ~

ABC ~ ADE

=AC

AE

AB

AD

ABC ~ ADE

JL LN

10

4

20

8

T

P

S

Q

U

R

50°30°

J

G

K

I

L

H

9 312

4

15

5

A

F

B

E

CD

A

B

C

D

E


Complete the following.

xx

yy

O

J

K L M

N


15. In the figure below, points and are the midpoints of the

(a) Find the slope of and the slope of .JL LN

slope of :JLKL

JK−JK

KL

JK

KL−KL

JK

slope of :LN −MN

LM

LM

MN−LM

MN

MN

LM

(b) It can be shown that .

Based on this, choose the ratio that is equal to .

JKL ~ LMNJK

KL

LM

MN

LN

MN

LM

LN

MN

LM

(c) Using the results above, choose the correct statement below.

slope of slope of JL = − LN

slope of slope of JL = LN

slope of slope of JL · LN = 1

slope of slope of JL · LN = − 1

(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.

The slopes of the two lines are opposites.

The slopes of the two lines are the same.

The slopes of the two lines are negative reciprocals.

The slopes of the two lines are reciprocals.


15. In the figure below, points , , and are the midpoints of the sides of .

Suppose , , and .Find the following lengths.

_____

_____

_____

16. In , . Given that , , and , find .

17. Use the given information to complete the proof of the following theorem.

J K L XYZ

=XZ 26 =KL 44 =YZ 78

=JK

=XY

=JY

PQR PQ ST =RP 28 =PQ 49 =ST 28 RS

XY

Z

J

KL

R

T

P Q

S


17. Use the given information to complete the proof of the following theorem.

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sidesproportionally.

Given:

Prove:

18. Find the value of each variable.

DC GF

=DG

GE

CF

FE

Statement Reason

1 DC GF Given

2 =~∠EDC ∠EGF _______________

3 =~∠E ∠ Reflexive Property

4 ~CDE FGE _______________

5 =DE

GE FECorr. sides of similar triangles are proportional 4

6 =DE +DG GE _______________

7 =CE +CF FE _______________

8 =+DG GE

GE

+FE

Substitution Property (Using 3 lines) 5 6 7

9 =+DG

GE

GE

GE+

CF

FE

FE

FEFraction Algebra 8

10 =+DG

GE1 +

CF

FE1 Fraction Algebra 9

11 =DG

GE FE_______________

Line(s) Used

F G

E

C D


18. Find the value of each variable.Simplify your answers as much as possible.

_____

_____

=x

=y

4x

23

4

8

9

y


Chapter 7 Practice Test #1 Answers for class M29 Geometry -2019-20 Term 2

1.

2.

(a) The arrows below show that the coordinates on the left are mappedto the coordinates on the right. Fill in the blanks to give thecoordinates after the dilation.

original coordinates final coordinates

(b) Choose the general rule below that describes the dilation mapping to .

3.

→X , −1 4 → X ' , −3 12Y , 3 2 → Y ' , 9 6

Z , −3 −1 → Z ' , −9 −3

XYZ X 'Y 'Z '

, x y → , 3y 3x , x y → , 3x y

, x y → , x 3y , x y → , 13 x

13 y

, x y → , 13 y

13 x , x y → ,

13 x 3y

, x y → , 3x 3y , x y → , 3x13 y

xx

2 4 6 8 10 12 14 16 18

yy

2

4

6

8

10

12

14

16

18


3.

Endpoints of original figure:

Left: Right:

Endpoints of final figure:

Left: Right:

4.

Dilation

, 1 5 , 4 4

, 3 15 , 12 12

xx

2 4 6 8 10 12 14 16 18 20

yy

2

4

6

8

10

12

14

16

18

20

0


4.

5.

6. Scale factor:

7.

8.

9.





=x 4.2

17

72

m∠ J =60 °m∠ K =25 °m∠ L =95 °


9.

(a) The height of the real table is inches. What is the height ofthe table in the scale model?

centimeters

(b) In the scale model, the length of the table is centimeters.What is the length of the real table?

inches

10.

11.

12. Not similar or not necessarily similar

Similar: , by the








Similar: , by the



13.

18

2

4

36

5

147 m

STU ~ QPR

JKL ~

ABC ~ FED

10

4

20

8

T

P

S

Q

U

R

50°30°

J

G

K

I

L

H

9 312

4

15

5

A

F

B

E

CD


13.

14.

15.

Statement Reason Line(s) Used

1 =A C

A E

A B

A DGiven

2 =~∠ A ∠ A Reflexive Property

3 ~A B C A D E SAS Similarity Property 1 2

(a) Find the slope of and the slope of .JL LN

slope of :JLKL

JK−JK

KL

JK

KL−KL

JK

slope of :LN −MN

LM

LM

MN−LM

MN

MN

LM

(b) It can be shown that .

Based on this, choose the ratio that is equal to .

JKL ~ LMNJK

KL

LM

MN

LN

MN

LM

LN

MN

LM

(c) Using the results above, choose the correct statement below.

slope of slope of JL = − LN

slope of slope of JL = LN

slope of slope of JL · LN = 1

slope of slope of JL · LN = − 1

(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.

The slopes of the two lines are opposites.

The slopes of the two lines are the same.

The slopes of the two lines are negative reciprocals.

The slopes of the two lines are reciprocals.


15.

16.

17.

18.

=JK 39

=XY 88

=JY 44

=RS 16

Statement Reason

1 DC GF Given

2 =~∠EDC ∠EGF If lines , then corr. s ∠ =~ 1

3 =~∠E ∠E Reflexive Property

4 ~CDE FGE AA Similarity Property 2 3

5 =DE

GE

CE

FECorr. sides of similar triangles are proportional 4

6 =DE +DG GE Segment Addition Property

7 =CE +CF FE Segment Addition Property

8 =+DG GE

GE

+CF FE

FESubstitution Property (Using 3 lines) 5 6 7

9 =+DG

GE

GE

GE+

CF

FE

FE

FEFraction Algebra 8

10 =+DG

GE1 +

CF

FE1 Fraction Algebra 9

11 =DG

GE

CF

FEAddition and Subtraction Properties 10

Line(s) Used

=x 6=y 3


chapter 7 practice test #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/...chapter 7...

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