similarity practice - washingtonville central school district · order on a line so that ab = 2bc =...

G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 1

Name: __________________________________________________________ Date: __________________

Similarity

Practice


I will know how to identify corresponding angles and

sides based on similarity statements.

I will know how to develop and write similarity

statements for two polygons.

I will know how to find missing measurements in similar

polygons.

I will know how to determine if two triangles are similar

based on their corresponding parts.

I will know how to establish a sequence of similarity

transformations between two similar polygons.

I will know how to prove two triangles are similar by AA,

SAS, and SSS criteria.


1. Solve each proportion using cross products.

a) b) c) d) 3

5 15

x

x = _______

1 6

15x x

x = _______

20 6

4

x

x

x = _______

4 2

12 2 13

x

x

x = _______

e) f) g) h) 1 1

6

x x

x

x = _______

3 9

4 7x

x = _______

9 2

5

x

x

x = _______

4

5 16

x

x = _______

2. Solve the following problems. (Show work)

a) The ratio of seniors to juniors in the Chess Club is 2:3. If there are 24 juniors, how many seniors are in the club?

b) A picture is 3 in. wide by 5 in. high was enlarged so that the width was 15 inches. How high is the enlarged picture?

c) A triangle’s three angles are in the ratio of 5:7:8. What is the measure of the smallest angle?


3. What would be the best (most specific) name for the shape that has the following ratios for its SIDES.

a) 3 : 4 : 3 _________________________ b) 4 : 5 : 4 : 5 ______________ or _____________ c) 3 : 3 : 5 : 5 _________________________ d) 5: 5: 5: 5 ______________ or _____________

4. What would be the best (most specific) name for the shape that has the following ratios for its ANGLES.

a) 3 : 4 : 3 _________________________ b) 4 : 5 : 4 : 5 ______________ or _____________ c) 2 : 2 : 7 : 7 _________________________ d) 4 : 4 : 4 : 4 ______________ or _____________

5. Solve the following problems. (Show work)

a) The ratio of two supplementary angles is 4:5. Find the measures of each angle.

b) A 3 foot stick is broken into two pieces. The ratio of the two pieces is 5:7. How big are the two pieces?

c) Points A, B, C, and D are placed in alphabetical order on a line so that AB = 2BC = CD. What is the ratio BD : AD?

d) Two numbers are in ratio 7 : 3. The sum of the two numbers is 36. What is the largest number?


1. Name the similarity transformations - What makes them different from the isometric transformations?

2. Why are isometric transformation a part of the similarity transformations?

3. Determine whether the following are (T)rue or (F)alse.

a) Similarity transformations are all isometric transformations. T or F b) Rotation is a similarity transformation. T or F c) All transformations are isometric. T or F d) Dilation is a non-isometric transformation. T or F e) Stretch is not a similarity transformation. T or F

4. Given that AFG DRH. Complete the following.

H ______ DR DH

AF ______ D ______

AG

RH DH ______

5. Pentagon ABCDE is similar to Pentagon RYMNT. Complete the following.

C ______ AB ED

RY ______

MN CD

RT ______

T ______ NT RT

DE ______

AB RY

BC ______

6. ABC is similar to another triangle. Provided is some information about the two triangles, BC AB

DR TD . From

this information determine the triangle similarity statement.

ABC _________

7. The two figures in each question are similar. Create the similarity statement from the diagram.

a) Pentagon GYKMR ____________ b) JMT __________ c) BAC __________

M

N

TR

YB

A

E

D

C

M

K

YG

R

BA

E D

C

J

T

MA

C

BO J

T

H

A

B

C


8. Determine the sequence of similarity transformations that map one figure onto the other thus establishing that the two figures are similar. a) Determine two similarity transformations that would map Quad. OBCD onto Quad. OHTE. ____________________ followed by _________________

b) Determine two similarity transformations that

would map OBC onto GT. ____________________ followed by _________________

c) Determine two similarity transformations that would map Quad. GHIJ onto Quad. RKYT. ____________________ followed by _________________

d) Determine two similarity transformations that

would map MNT onto RFH. ____________________ followed by _________________

O

T

E

H

B C

D

G

T

O

C

B

T

Y

R

I

H

G

J

O

K

H

R

N

M

T

F


9. Jose claims that he was able to do 4 different double similarity transformations to map CDE onto MPN. Let us see if you can do 4 as well. (Show the steps) a) Method #1 ____________________ followed by _________________

b) Method #2 ____________________ followed by _________________

c) Method #3 ____________________ followed by _________________

d) Method #4 ____________________ followed by _________________

P

M

C

E

D

N

P

M

C

E

D

N

P

M

C

E

D

N

P

M

C

E

D

N


1. Solve for the missing information, given that the two triangles in each question are SIMILAR.

a) b) c)

x = ___________ y = __________

x = ___________ y = __________

x = ___________ y = __________ d) e) f)

x = ___________ y = __________

x = ___________ y = __________

ABC has sides of 5,6,7

ABC DEF

DEF has sides 9, x, y

x = ___________ y = __________

2. If the three sides of a triangle are in ratio of 3:5:7 and the perimeter of the triangle is 12 cm. What is the

length of the longest side?

y

10.8

x

6

12

10

T

G

R

S

Q

y

10

x

124

8

W

T

V

X

U

α

α

o

ox

36

y

16

12

21

186

y

15x

20

W

T

V

X

U

y

20

9

5b

3b

x

o

o


3. Use the scale factor to determine the missing values.

a) LMN : LJK is 1:2 b) QNP : HRT is 2:1

x = ____________ y = __________

x = ____________ y = __________

4. Use the Pythagorean Theorem to help you on these. Solving for the missing values.

a) b)

x = ___________ y = __________

Right ABC has sides of AB = 8, BC = 15, & AC = x

where AC is the hypotenuse

ABC DEF

Right DEF has sides DE = z, EF = y, & DF = 51

x = ___________ y = __________ z = ___________

y

3

x

4

o

o

M

J

L

K

N

Y

X

24

21

20°20°

P

Q

NR

H

T

y

x

4

3

6

3


1. Prove that if two triangles have two congruent corresponding angles, then they must be similar.

Given: A P and C N Prove: ABC PMN

2. Prove that if two triangles have two corresponding proportional sides and the included corresponding

congruent angle (SAS) is enough for establishing similarity.

Given: A P and PM PN

AB AC Prove: ABC PMN

3. Prove that for two triangles to be similar we need to find a sequence of similarity transformations that map

ABC on to DEF.

Given: PM PN MN

AB AC BC Prove: ABC PMN

x

x

o

o

M

N

P

A

B

C

o

o

P

M

N

A

B

C

N

P

M

B

A

C


4. By construction, use similarity constructions to map ABC onto NMP.

(Hint: ,2BD ABC first and then reflect.) (There are many ways to do this construction)

5. By construction, use similarity construction to map ABC onto NPM.

(Hint: 1,2

BD ABC first and then rotate.) (There are many ways to do this construction)

x

o

x

o

P

N

M

A

B

C

P

M

N

A

C

B


1. Are the following pairs of triangles similar? If they are, then name their similarity criteria. (SSS, SAS, AA)

a) Yes / No __________ b) Yes / No __________ c) Yes / No __________

d) Yes / No __________ e) Yes / No __________ f) Yes / No __________

2. Are the following pairs of triangle similar? If YES, name the similarity criteria (SSS, SAS, AA)

a) Yes / No

Criteria ________

b) Yes / No

Criteria ________

c) Yes / No

Criteria ________

d) Yes / No

Criteria ________

e) Yes / No

Criteria ________

f) Yes / No

Criteria ________

g) Yes / No

Criteria ________

h) Yes / No

Criteria ________

3. Jeff asks the teacher is ASA is also a similarity criterion. The teacher says yes but it isn’t needed. Why

isn’t it needed?

o

o

5.62.8

7

3.5

8

4

60°

57°

53°

57°

20°15° θx

o

o

10

16

4

6

o

o

o

o7.54.5

5 393°

93°

16

20

15

8

6

12

o

o

9 612

8


4. Are the following pairs of triangle similar? If YES, name the similarity criteria (SSS, SAS, AA) and create a

similarity statement. If NO, just circle No.

a) Yes / No

Criteria ________

_____ _____

b) Yes / No

Criteria ________

_____ _____

c) Yes / No

Criteria ________

_____ _____

d) Yes / No

Criteria ________

_____ _____

5. Prove the following relationships.

a) GIVEN: LN = 4 cm, KL = 5 cm LY = 12 cm, LH = 15 cm

PROVE:

KLN HLY

b) GIVEN: G HIJ

PROVE:

FGH JIH

STATEMENT REASON

STATEMENT REASON

c) GIVEN: ABCD is a parallelogram

PROVE:

AHE FHG

d) GIVEN:

1 2 & AC AE

PROVE:

CBD EFD

STATEMENT REASON

STATEMENT REASON

96°

21°63°

63°

H

G

R

E

D

F

T

G

R

S

Q

o

W

T

V

X

U 8.25

4 5.5

9.9

6.64.8

P

O

N

T

R

H

12

154

5K

H

L

N

Y

o

o

F H

G

I

J

H

BA

D C

FG

E

2

1

B

A

C

E

D

F


2. Prove the following relationships.

a) GIVEN: PQ PR

PT PS

PROVE:Q

b) GIVEN: U ZTW

PROVE: UV WU

TZ WT

STATEMENT REASON

STATEMENT REASON

c) GIVEN:

||AB DC

PROVE:

GA GC = GB GH

d) GIVEN: FG = 7 cm, GH = 8 cm, FH = 10 cm CB = 14 cm, BA = 16 cm, AC = 20 cm

PROVE:

F C

STATEMENT REASON

STATEMENT REASON

e) GIVEN: TH TL

TJ TK

PROVE: ||HL KJ

f) GIVEN: TUW TVX

PROVE:TU TW

TV TX

STATEMENT REASON

STATEMENT REASON

P

Q R

S To

o

W

V

U

Z

T

G

BA

D H

C20

14

16

10

87

A

C

BF

G

H

T

H

KL

J

o

o

W

T

V

X

U

similarity practice - washingtonville central school district · order on a line so that ab = 2bc =...

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