1. 6.6 Inequalities in Two Triangles

2. What We Will Learn
Compare measures in triangles
Proofs
Story problems

3. Exs. 1/2 Using Hinge Thm and Converse
Given that 𝑆𝑇 ≅ 𝑃𝑅 , how does 𝑚∠𝑃𝑆𝑇 compare to 𝑚∠𝑆𝑃𝑅?
𝑃𝑆 ≅ 𝑃𝑆 by reflex. Prop and PT is greater than RS
∠𝑃𝑆𝑇>∠𝑆𝑃𝑅 by 6.13
Given that 𝐽𝐾 ≅ 𝐿𝐾 , how does JM compare to LM?
𝐾𝑀 ≅ 𝐾𝑀 by reflex prop. ∠𝐽𝐾𝑀>∠𝐿𝐾𝑀.
𝐽𝑀 > 𝐿𝑀 by 6.12

4. Exs. 3/4 Proofs Given: ∠𝑋𝑊𝑌≅∠𝑋𝑌𝑊, 𝑊𝑍 > 𝑌𝑍 Prove: 𝑚∠𝑊𝑋𝑍>𝑚∠𝑌𝑋𝑍
Statement
Reason
1. ∠𝑋𝑊𝑌≅∠𝑋𝑌𝑊, 𝑊𝑍 > 𝑌𝑍
1. Given
2. 𝑋𝑍 ≅ 𝑋𝑍
2. Reflex Prop
3. 𝑊𝑋 ≅ 𝑋𝑌
3. Thm 5.7
4. 𝑚∠𝑊𝑋𝑍>𝑚∠𝑌𝑋𝑍
4. Thm 6.13

5. Ex. 5 Story Problem
Two groups of bikers leave the camp heading in opposite directions. Each group travels 2 miles, then changes direction and travels 1.2 miles. Group A starts due east and then turns 45 degrees toward north. Group B starts due west and then turns 30 degrees toward south. Which group if farther from camp?
Draw diagram
Use Hinge Thm or Converse of Hinge
Group B

6. Your Practice
Your flight: Flies 100 miles due west, then turns 20 degrees toward north and flies 50 miles.
Friend’s flight: Flies 100 miles due north, then turns 30 degrees toward east and flies 50 miles.
Who is farther away?
Your flight