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Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 Section 83 : Proving Triangles Similar Warm Up Name the postulate or theorem you use to prove the triangles congruent. 3. 2. 1. Postulate 81 : AngleAngle Similarity (AA ~) Postulate : If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. T P R TRS ~ PLM S L M 1 Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 Example 1) Explain why the triangles are similar. Write a similarity statement. V o 45 W S 45o B R Do we have enough information to write a similarity statement or a similarity ratio? Theorem 81 : SideAngleSide Similarity (SAS ~) Theorem : If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar. 5 10 3 6 2 Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 Theorem 82 : SideSideSide Similarity (SSS ~) Theorem : If the corresponding sides of two triangles are proportional, then the triangles are similar. 2 3 6 9 4 6 Example 2) Explain why the triangles must be similar. Write a similarity statement. Z P 6 Q 3 R 8 X 4 Y 3 Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 You try) Explain why the triangles must be similar. Write a similarity statement. 9 B A G 6 6 C 8 8 E 12 F Example 3) Explain why the triangles are similar. Write a similarity statement. Then find DE. A 10 12 24 D C 16 B 18 E 4 Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 You can use similar triangles and measurements to find distances that are difficult to measure directly. This is called indirect measurement. One method of indirect measurement uses the fact that light reflects off a mirror at the same angle at which it hits the mirror. A second method uses the similar triangles that are formed by certain figures and their shadows. (See next examples.) Example 4) Ramon places a mirror on the ground 40.5 ft 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 the point, Ramon's eyes are 6 ft above the ground and he is 7 ft from the image in the mirror. Use similar triangles to find the height of the geyser. 5 Geometry Lesson 83 Proving Triangles Similar.notebook January 24, 2013 You try) In sunlight, a cactus casts a 9ft shadow. At the same time a person 6 ft tall casts a 4ft shadow. Use similar triangles to find the height of the cactus. 6