5 - 6 I N E Q U A L I T I E S I N T W O T R I A N G L E S

CHAPTER 5

OBJECTIVES

• Apply inequalities in two triangles.

INEQUALITIES THEOREMS

EXAMPLE 1A: USING THE HINGE THEOREM AND ITS CONVERSE

• Compare mBAC and mDAC.

• Compare the side lengths in ∆ABC and ∆ADC.• AB = AD AC = AC BC > DC• By the Converse of the Hinge Theorem, mBAC >

mDAC.

EXAMPLE

• Compare EF and FG.

Compare the sides and angles in ∆EFH angles in ∆GFH.

mGHF = 180° – 82° = 98°

EH = GH FH = FH mEHF > mGHF

By the Hinge Theorem, EF < GF

EXAMPLE

• Compare mEGH and mEGF.

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.• m1 = m2 • m3 > m4 • Prove: AB > ED

1. Given

2. Def. of Midpoint

3. Def. of s

4. Conv. of Isoc. ∆ Thm.

5. Hinge Thm.

1. C is the mdpt. of BDm3 > m4, m1 = m2

3. 1 2

5. AB > ED

Statements Reasons

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