1 / 16

5-6

5-6. Inequalities in Two Triangles. Holt Geometry. Warm Up 1. Write the angles in order from smallest to largest. 2. The lengths of two sides of a triangle are 12 cm and 9 cm. Find the range of possible lengths for the third side. Objective. Apply inequalities in two triangles.

emilia
Télécharger la présentation

5-6

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. 5-6 Inequalities in Two Triangles Holt Geometry

  2. Warm Up 1.Write the angles in order from smallest to largest. 2. The lengths of two sides of a triangle are 12 cm and 9 cm. Find the range of possible lengths for the third side.

  3. Objective Apply inequalities in two triangles.

  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 1B: Using the Hinge Theorem and Its Converse Compare EF and FG.

  6. Example 1C: Using the Hinge Theorem and Its Converse Find the range of values for k. Step 1 Compare the side lengths in ∆MLN and ∆PLN.

  7. Example 2: Travel 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 S 10º E. Who is farther from school? Explain.

  8. Example 3: Proving Triangle Relationships Write a two-column proof. Given: Prove: AD > CB Proof: 1. Given 2. Reflex. Prop. of  3. Hinge Thm.

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

  10. Proof: 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.

  11. Check It Out! Example 3b Write a two-column proof. Given: SRT  STR TU > RU Prove: mTSU > mRSU 1. Given 1.SRT  STR TU > RU 2. Conv. of Isoc. Δ Thm. 3. Reflex. Prop. of  4. mTSU > mRSU 4. Conv. of Hinge Thm.

  12. Lesson Quiz: Part I 1. Compare mABCand mDEF. 2. Compare PS and QR.

  13. Lesson Quiz: Part II 3. Find the range of values for z. –3 < z < 7

  14. 1. Given 2. Reflex. Prop. of  3. Conv. of Hinge Thm. 3. mXYW <mZWY Lesson Quiz: Part III 4. Write a two-column proof. Prove: mXYW <mZWY Given: Proof:

More Related