1. Sections 8-3/8-5: April 24, 2012

2. Warm-up: (10 mins) Practice Book: Practice 8-2 # 1 – 23 (odd)

3. Warm-up: (10 mins)

5. Questions on Homework?

6. Review Name the postulate you can use to prove the triangles are congruent in the following figures:

7. Sections 8-3/8-5: Ratio/Proportions/Similar Figures Objective: Today you will learn to prove triangles similar and to use the Side- Splitter and Triangle-Angle-Bisector Theorems.

8. Angle-Angle Similarity (AA ∼ ) Postulate  Geogebra file: AASim.ggb

9. Angle-Angle Similarity (AA ∼ ) Postulate

10. Example 1: Using the AA ∼ Postulate, show why these triangles are similar  ∠ BEA ≅∠ DEC because vertical angles are congruent  ∠ B ≅∠ D because their measures are both 600  ΔBAE ∼ ΔDCE by AA ∼ Postulate.

11. SAS ∼ Theorem ΔABC ∼ ΔDEF

12. SAS ∼ Theorem Proof

13. SSS ∼ Theorem

14. SSS ∼ Theorem Proof

15. Example 2: Explain why the triangles are similar and write a similarity statement.

16. Example 3: Find DE

17. Real World Example How high must a tennis ball must be hit to just pass over the net and land 6m on the other side?

18. Use Similar Triangles to find Lengths

19. Use Similar Triangles to Heights

20. Section 8-5: Proportions in Triangles Open Geogebra file SideSplitter.ggb

21. Side-Splitter Theorem

22. Example 4: Use the Side-Splitter Theorem to find the value of x

23. Example 5: Find the value of the missing variables

24. Corollary to the Side-Splitter Theorem

25. Example 6: Find the value of x and y

26. Example 7: Find the value of x and y

27. Sail Making using the Side-Splitter Theorem and its Corollary What is the value of x and y?

28. Triangle-Angle-Bisector Theorem

29. Triangle-Angle-Bisector Theorem Proof

30. Example 8: Using the Triangle-Angle- Bisector Theorem, find the value of x

31. Example 9: Fnd the value of x

32. Theorems  Angle-Angle Similarity (AA ∼ ) Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are 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 including the two angles are proportional, then the triangles are similar.  Side-Side-Side Similarity (SSS ∼ ) Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar.  Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.  Corollary to the Side-Splitter Theorem: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.  Triangle-Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

33. Wrap-up  Today you learned to prove triangles similar and to use the Side-Splitter and Triangle-Angle-Bisector Theorems.  Tomorrow you’ll learn about Similarity in Right Triangles Homework (H)  p. 436 # 4-19, 21, 24-28  p. 448 # 1-3, 9-15 (odd), 25, 27, 32, 33 Homework (R)  p. 436 # 4-19, 24-28  p. 448 # 1-3, 9-15 (odd), 32, 33