7 3 Proving Triangles Similar Objectives By the

7. 3 Proving Triangles Similar • Objectives • By the end of this lesson, I will be able to use the AA~ postulate, as well as the SAS~ and SSS~ Theorems when dealing with similar triangles • I will also be able to use similarity to ingeniously find indirect measurements

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.

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. Similar b. Not similar.

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.

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

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.

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.

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.

Finding the Length of Similar Triangles • Before rock climbing, Darius wants to know 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?

Finding Lengths in Similar Triangles Triangle HTV ~ Triangle JSV – AA~ Postulate

More Practice!!!!! • In-class practice: Textbook p. 455 – 456 # 7 – 12, 15, 16, 17. • Additional Assignment : Math. XL assignment (which includes tomorrow’s 7. 4 lesson) due Wednesday 1/13/2016 • Exit ticket…….