1. 5-6 inequalities in two triangles
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BAC and 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. mGHF = 180° – 82° = 98°
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EGH and 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 Statements Reasons 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. Statements Reasons 1. C is the mdpt. of BD m3 > m4, m1 = m2
1. Given
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