Chapter 5

1. Chapter 5 5-6 inequalities in two triangles

2. Objectives • Apply inequalities in two triangles.

3. Inequalities theorems

4. Example 1A: Using the Hinge Theorem and Its Converse • Compare mBACand mDAC. • Compare the side lengths in ∆ABC and ∆ADC. • AB = AD AC = AC BC > DC • By the Converse of the Hinge Theorem, mBAC > mDAC.

5. Example • Compare EF and FG. Compare the sides and angles in ∆EFH angles in ∆GFH. mGHF = 180° – 82° = 98° EH = GH FH = FH mEHF > mGHF By the Hinge Theorem, EF < GF

6. Example • Compare mEGHand mEGF.

7. Application • John and Luke leave school at the same time. John rides his bike 3 blocks west and then 4 blocks north. Luke rides 4 blocks east and then 3 blocks at a bearing of N 10º E. Who is farther from school? Explain.

8. solution • The distances of 3 blocks and 4 blocks are the same in both triangles. • The angle formed by John’s route (90º) is smaller than the angle formed by Luke’s route (100º). So Luke is farther from school than John by the Hinge Theorem.

9. Writing Proofs • Write a two-column proof. • Given: Prove: AB > CB

10. solution 1. Given 2. Reflex. Prop. of  3. Hinge Thm.

11. Example • Write a two-column proof. • Given: C is the midpoint of BD. • m1 = m2 • m3 > m4 • Prove: AB > ED

12. 1. Given 1.C is the mdpt. of BD m3 > m4, m1 = m2 2. Def. of Midpoint 3.1  2 3. Def. of  s 4. Conv. of Isoc. ∆ Thm. 5.AB > ED 5. Hinge Thm.

13. Videos

14. Student Guided Practice • Do problems 1-3 in your book page 355 • Do worksheet

15. Homework • DO problems 9-12 and 16 in your book page 355 and 356

16. Closure • Today we learned about hinge theorem and its converse • Next class we are going to learned about Pythagorean theorem