true or false??? two triangles are always similar. 10-2... · 2017. 10. 25. · 3 shortcuts to show...

True or False???If False, give a counterexample.

Two triangles are always similar.

True or False???If False, give a counterexample.

Two isosceles triangles are always similar.

Two equilateral triangles are always similar.

True or False???If False, give a counterexample.

True or False???If False, give a counterexample.

Two rectangles are always similar.

Two squares are always similar.

True or False???If False, give a counterexample.

True or False???If False, give a counterexample.

Two trapezoids are always similar.

Two isosceles trapezoids are always similar.

True or False???If False, give a counterexample.

True or False???If False, give a counterexample.

Two regular pentagons are always similar.

Two circles are always similar.

True or False???If False, give a counterexample.

HW Solutions p. 499­500# 2­26 even, 32, 34

2. False

4. True

6. False

8. True

10. True

12. 1/1000 = .001

14. QRST ~ XWZY; 3/4

16. ABCD ~ FGHE; 4/5

18. ABC ~ FED; 7/5

20. 32

22. 6 7/8 = 6.875

24. 14

26. -10 or 10

32. x = 16 y = 4.5 z = 7.5

34. 70 mm

Chapter 10 Similarity

10­2 Proving Triangles Similar

Objective: Use postulates and theorems to provetriangles similar.

Definition of Similar Figures

­­ all corresponding angles are congruent

­­ all corresponding sides are proportional

Recall:

We want to focus on similar triangles.

3 shortcuts to show two triangles are similar

Postulate 10­1 (AA ~ Post)

Angle­Angle Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

T

R S

P

LM

Theorem 10­1 (SAS ~ Thm)

Side­Angle­Side Similarity 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.

Theorem 10­2 (SSS ~ Thm)

Side­Side­Side Similarity Theorem

If the corresponding sides of two triangles are proportional, then the triangles are similar.

Are these triangles similar? Why?

R

WS

V

B

45° 45°

6

6

9 8 8

12

HW # 104p. 507­508 # 1­12, skip #10

Due By End of Class!!