5-6 inequalities in two triangles chapter 5. objectives apply inequalities in two triangles
TRANSCRIPT
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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
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OBJECTIVES
• Apply inequalities in two triangles.
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INEQUALITIES THEOREMS
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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.
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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
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EXAMPLE
• Compare mEGH and mEGF.
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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.
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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.
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WRITING PROOFS
• Write a two-column proof.• Given:
Prove: AB > CB
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SOLUTION
Statements Reasons
1. Given
2. Reflex. Prop. of
3. Hinge Thm.
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EXAMPLE
• Write a two-column proof.• Given: C is the midpoint of BD.• m1 = m2 • m3 > m4 • Prove: AB > ED
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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
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VIDEOS
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STUDENT GUIDED PRACTICE
• Do problems 1-3 in your book page 355 • Do worksheet
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HOMEWORK
• DO problems 9-12 and 16 in your book page 355 and 356
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CLOSURE
• Today we learned about hinge theorem and its converse
• Next class we are going to learned about Pythagorean theorem