6.6 Inequalities in Two Triangles

What We Will Learn Compare measures in triangles Proofs Story problems

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

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

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

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