6th Grade Math Textbook, Fundamentals

Lesson 6-7 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

1. Figure MNOPis similar to figure ZYWX.

Find the length of NM.

2.FGHTUV. Angle Fmeasures 90°, angle G measures 30°,

and angle Hmeasures 60°. What is the measure of angle U?

3.Discuss and Write How can you use the lengths of the sides to determine

whether two figures are similar? Use an example to explain your answer.

ACand BCof BAC are equal in length. If GFH

and BACare similar, what is the length ofHF?



Let ythe length of side HF.

Solve:  Check:

1.5 • 4  2 y 1.5(4) 2(3)

6  2  2 y 26  6 Tr u e

3 y

So the length of HFis 3 feet.

?

?^3

4

1. 5
   2

y

4

1. 5
   2

HF

CA

GF

BA

1

In similar figures, the lengths of the corresponding sides are proportional.

Therefore, you can use proportions to find missing dimensions of similar figures.

What is the length of TS, if figure ABCDis similar to figure UTSR?

To find the length of TS:

• Identify pairs of corresponding sides.
  ADcorresponds to UR.
  BCcorresponds to TS.


• Write and solve a proportion.



Let xthe length of side TS.

Solve: 

10 x 48 Cross multiply.

10 x  10  48  10 Divide both sides by 10.

x4.8

So the length of side TSis 4.8 meters.

6 m

x

10 m

8 m

BC

TS

AD

UR

10 m

6 m

3.5 m

AD

B C

8 m

2.8 m

x

UR

T S

Check:

10(4.8) 8(6)

4.8 4.8 Tr u e

?

? 6 m

4.8 m

10 m

8 m

Think

Side GFcorresponds to side BA.

Side HFcorresponds to side CA.

Side GHcorresponds to side BC.

9 cm

15 cm

Z

X

Y

W

N 5 cm

M

O

P

1.5 ́

F y

G

H

4 ́

A 2 ́

C

B