“Why so serious?”

7.3 Proving Triangles Similar

Similar Triangles

80° 40° 80° 40°

Postulate 7-1: Angle-Angle Similarity (AA ~) Postulate: If two angles of one triangle are congruent to two angles of another, then the triangles are similar.

TRS ~ PLM

Similar Triangles

R

W

S

B

V

Statements Reasons

1.

2.

3.

1.

2.

3.

RV

RSW VSB

RWS ~ VBS

Given : RVProve : RWS ~ VBS

Similar Triangles

Theorem 7-1: Side-Angle-Side Similarity (SAS ~) Theorem: If an angle of one triangle is congruent to an angle of a second, and the sides including the two angles are proportional, then the triangles are similar.

Theorem 7-2: Side-Side-Side Similarity (SSS ~) Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar.

Similar Triangles

If the following triangles are similar, state which postulate/theorem tells us. Then, find DE.

Real World ConnectionRamon places a mirror on the ground and walks back until he can see the top of the geyser in the middle of the mirror. Use similar triangles to find the height of the geyser.

Similar Triangles

In sunlight, a cactus casts a 9-ft shadow. At the same time, a 6-ft person casts a 4-ft shadow. Use similar triangles to find the height of the cactus.

Review

32

Simplify.

50

27

105

86

Review

2128

2

144

3

75

4125

“I feel the need… the need for speed!

HW (7.3) Pgs. 386-390; #1-19 odd, 31-39 odd, 41

7.3 Proving Triangles Similar