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8.3: Proving Triangles Similar

8.3: Proving Triangles Similar. Objectives: To use and apply AA, SAS and SSS similarity statements To use indirect measurement and proportions to find missing measures. Angle-Angle Similarity (AA~)Postulate.

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8.3: Proving Triangles Similar

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  1. 8.3: Proving Triangles Similar Objectives: To use and apply AA, SAS and SSS similarity statements To use indirect measurement and proportions to find missing measures

  2. Angle-Angle Similarity (AA~)Postulate If two angles of one triangle are congruent to two angles of another, then the triangles are similar

  3. Side-Angle-Side 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. E B A D C F

  4. Side-Side-Side Similarity (SSS~)Theorem If the corresponding sides of 2 triangles are proportional, then the triangles are similar. 6 6 8 8 3 4

  5. Explain why the triangles must be similar. Then write a similarity statement. T J C G K Z

  6. Are the triangles similar? If so, write a similarity statement and name the postulate or theorem you used. 1. (not drawn to scale) 2. A 10 25 X Y 30 75 C B

  7. Explain why the triangles are similar. Then find x. 1. x 24 14 22

  8. Are the two triangles similar? If so, state the theorem or postulate and write a similarity statement.

  9. Are the 2 triangles similar?

  10. Indirect Measurement • Use similar triangles and measurements to find distances that are difficult to measure directly • Fact: light reflects off a mirror at the same angle at which it hits mirror (creating similar triangles) • Fact: similar triangles are formed by certain figures and their shadows

  11. Example: 1. A fire hydrant 2.5 feet high casts a 5-foot shadow. How tall is a street light that casts a 26-foot shadow at the same time? Let h represent the height of the street light. 2. At 7 feet 2 inches, Margo Dydek is one of the tallest women to play professional basketball. Her coach, Carolyn Peck, is 6 feet 4 inches tall. If Ms. Peck casts a shadow that is 4 feet long, about how long would Ms. Dydek’s shadow be? Round to the nearest tenth.

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