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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.

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5-6

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  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:

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