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7.3 Proving Triangles Similar
• Angle-Angle Similarity (AA ~) Postulate– If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are similar.
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Using the AA ~ Postulate
• Are the two triangles similar? How do you know?a. Triangle RSW and Triangle VSB.b. Triangle JKL and Triangle PQR.
a. Similarb. Not similar.
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Side-Angle-Side Similarity (SAS ~) Theorem
• If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.
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Side-Side-Side Similarity (SSS ~ ) Theorem
• If the corresponding sides of two triangles are proportional, then the triangles are similar.
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Verifying Triangle Similarity
• Are the triangles similar? If so, write a similarity statement for the triangles.
• Yes, Triangle STU ~ Triangle XVW by the SSS Similarity Theorem.
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Verifying Triangle Similarity
• Are the triangles similar? If so, write a similarity statement for the triangles.
• Yes, Triangle KLP ~ Triangle KMN by the SAS Similarity Theorem.
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Indirect Measurement
• You can use indirect measurement to find lengths that are difficult to measure directly.– One method of indirect measurement uses the
fact that light reflects off a mirror at the same angle at which it hits the mirror.
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Finding the Length of Similar Triangles• Before rock climbing, Darius wants to know how high he will climb.
He places a mirror on the ground and walks backward until he can see the top of the cliff in the mirror. What is the height of the cliff?
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Finding Lengths in Similar Triangles
~ ~HTU JSV AA Postulate HT TV
JS SV
5.5 6
34x
187 6x 31.2x
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More Practice!!!!!
• Homework – Textbook p. 455 – 456 # 7 – 12, 15, 16, 17.