1 / 16

Chapter 5

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 .

gittel
Télécharger la présentation

Chapter 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 5 5-6 inequalities in two triangles

  2. Objectives • Apply inequalities in two triangles.

  3. Inequalities theorems

  4. Example 1A: Using the Hinge Theorem and Its Converse • Compare mBACand 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.

  5. Example • Compare EF and FG. 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

  6. Example • Compare mEGHand mEGF.

  7. 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.

  8. 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.

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

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

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

  12. 1. Given 1.C is the mdpt. of BD m3 > m4, m1 = m2 2. Def. of Midpoint 3.1  2 3. Def. of  s 4. Conv. of Isoc. ∆ Thm. 5.AB > ED 5. Hinge Thm.

  13. Videos

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

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

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

More Related