5-6 inequalities in two triangles Chapter 5 5-6 inequalities in two triangles

Objectives Apply inequalities in two triangles.

Inequalities theorems

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.

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

Example Compare mEGH and mEGF.

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.

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.

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

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

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

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.

Videos

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

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

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