Objective Apply inequalities in two triangles..

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Example 1A: Compare mBAC and mDAC. Compare the side lengths in ∆ABC and ∆ADC. By the Converse of the Hinge Theorem, mBAC > mDAC. AB = AD AC = AC BC.

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Presentation transcript:

Objective Apply inequalities in two triangles.

Example 1A: Using the Hinge Theorem and Its Converse Compare mBAC and mDAC.

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

Example 1C: Using the Hinge Theorem and Its Converse Find the range of values for k.

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 N 10º E. Who is farther from school? Explain.

Example 3a: Proving Triangle Relationships Write a two-column proof. Given: Prove: AD > CB Proof:

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

Check It Out! Example 3c Write a two-column proof. Given: SRT  STR TU > RU Prove: mTSU > mRSU