7th Grade Math

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Similarity and Proportional Reasoning

PART A BCDE

Multi-Part

Lesson 3

GLE 0706.4.1

Understand the application

of proportionality with

similar triangles.

SPI 0706.4.1 Solve

contextual problems

involving similar triangles.

Also addresses GLE 0706.1.1,

GLE 0706.1.3, SPI 0706.4.2.

Lesson 3A Similarity and Proportional Reasoning 293

Main Idea

Solve problems

involving similar

figures.

Vocabulary

similar figures

corresponding sides

corresponding angles

indirect measurement

Side-Side-Side Similarity

(SSS)

Angle-Angle Similarity

(AA)

Side-Angle-Side

Similarity (SAS)

Similar Figures

Each pair of figures below have the same shape

but different sizes. Copy each pair onto centimeter dot paper.

Measure each side using a centimeter ruler.

E

D

A

C

B

H

F

GT

Y Z

X

S

R

1.

−−

AB is in the same relative position as

−−

EF. Name all such pairs of

sides in each pair of figures.

The notation −−AB means the segment with endpoints at A and B.

2. Write each ratio in simplest form.
   The notation AB means the measure of segment AB.

a. _ ABEF ; FGBC ; (^) HGDC ; ADEH b. (^) XYRS ; _YZST ; _RTXZ

3. What do you notice about the ratios of these sides?


4. Name all pairs of angles in the same relative position. Cut out the
   figures. Compare the angles by matching them up. What do you
   notice about the measure of these angles?


5. MAKE A CONJECTURE Write a sentence about the sides and angles
   that are in the same position.

Figures that have the same shape but not necessarily the same size are

similar figures. Triangle RST is similar to triangle XYZ.

118 ° 36 °

26 °

4 cm

3 cm

6 cm

3

4

5

9

:

;

2 cm

3 cm

1.5 cm

26 °

36 °

118 °

Corresponding sides — −−ST and −−YZ , −−SR and −−YX , and −−RT and −−XZ —

are sides that are in the same relative position.

Corresponding angles — ∠S and ∠Y, ∠R and ∠X, and ∠T and ∠Z —

are angles that are in the same relative position.

V

s

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293_303_C05_L3_895130.indd 293 12/29/09 1:09 PM