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

6. Are the triangles similar
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
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.