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
W
V
Given : R  V
S
Prove : RWS ~ VBS
R
Statements
Reasons
1. R  V
1.
2. RSW  VSB
2.
3. RWS ~ VBS
3.
B
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, give the similarity
statement and state which postulate/theorem tells us.
Then, find DE.
What is the similarity ratio from the larger triangle to
the smaller triangle?
Similar Triangles
If the following triangles are similar, give the similarity
statement and state which postulate/theorem tells us. If
they are not similar, explain why not.
Real World Connection
Ramon 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.