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Chapter 8 – Similarity
Lesson 3 - Proving Triangles Similar (p. 432)
The AA Postulate and the SAS and SSS Theorems

Indirect Measurement
Postulate 8-1 - Angle-Angle Similarity (AA~) – If two angles of one triangle are congruent to
two angles of another triangle, then the triangles are similar.
TRS ~ PLM
- Using the AA~ Postulate
a. Explain why the triangles are similar. Write a similarity statement.
b. Do you have enough information to find the similarity ratio?
Theorem 8-1 - Side-Angle-Side Similarity (SAS~) – If an angle of one triangle is congruent to
an angle of a second triangle, and the sides including the two triangles are proportional, then the
triangles are similar.
Theorem 8-2 - Side-Side-Side Similarity (SSS~) – If the corresponding sides of two triangles
are proportional, then the triangles are similar.
- Using Similarity Theorems
a. Explain why the triangles must be similar. Write a similarity statement.
b. Explain why the triangles must be similar. Write a similarity statement.
Lesson 3 – Proving Triangles Similar
Page 1
Revised Fair 2014-2015
Chapter 8 – Similarity
Applying AA, SAS, and SSS Similarity
- Finding Lengths in Similar Triangles
a. Explain why the triangles are similar. Write a similarity statement, and then find DE.
b. Find the value of x in the figure.
- Real-World Connection
a. Ramon places a mirror on the ground 40.5ft from the base of a geyser. He walks
backwards until he can see the top of the geyser in the middle of the mirror. At that
point, Ramon’s eyes are 6ft above the ground and he is 7ft from the image in the
mirror. Use similar triangles to find the height of the geyser.
b. In sunlight, a cactus casts a 9ft shadow. At the same time a person 6ft tall casts a 4ft
shadow. Use similar triangles to find the height of the cactus.
Lesson 3 – Proving Triangles Similar
Page 2
Revised Fair 2014-2015