Page 105 - Math Course 3 (Book 2)

Similar Triangles
Mo. 9

Lesson 8 Key Concept

Similar Triangles
KEY CONCEPTS:

1. Determine whether two triangles are similar. Words If two triangles are similar, then the
2. Find the unknown measures of sides of two measures of their corresponding sides
similar triangles. are proportional, and the measures of
their corresponding angles are equal.

AB BC AC
Symbols △If ABC? △DEF, then = =
MO. 9 - L8a DE EF DF
Model
B E
Identifying Similar Triangles

A C
D F
Vocabulary A-Z

Let us learn some vocabulary

Let’s Begin
similar triangles
Similar triangles have the same shape, but not
necessarily the same size. There are two main
tests for similarity. Determine Whether Two Triangles Are Similar

• If the angles of one triangle and the corresponding
angles of a second triangle have equal measures, Example
then the triangles are similar.

Determine whether the pair of triangles is similar.
• If the measures of the sides of two triangles form
equal ratios, or are proportional, then the triangles Justify your answer.
are similar. Y

12
E 15
B Z
4 cm 5 cm
2 cm 2.5 cm 830 X
830 B 24
560 410 D 560 410 F
A C 10 8
3 cm 6 cm
Corresponding angles Corresponding sides A C
16
AB 2 1 15 3
∠A and ∠D AB and DE → = = 2 The ratio of sides XY to AB is or
4
DE
∠B and ∠E 10 2
2.5
BC
∠C and ∠F BC and EF → = = 1 The ratio of sides YZ to BC is 12 3
or
5
2
EF
2
8

AC 3 1 The ratio of sides XZ to AC is 24 3
or
AC and DF → = = 2 16 2
DF
6
Similar Triangle are triangles whose The corresponding sides of the
corresponding angle are congruent and Answer triangles are proportional, so the
whose corresponding sides are in proportion. triangles are similar.
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