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Solving Inequalities in Triangles Through Hinge Theorem Applications

Learn how to apply inequalities in triangles using the Hinge Theorem and Its Converse with various examples and proofs. Discover the range of values, analyze travel scenarios, and understand triangle relationships. Improve your geometry skills today!

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Solving Inequalities in Triangles Through Hinge Theorem Applications

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  1. Objective Apply inequalities in two triangles.

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

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

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

  5. 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.

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

  7. 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

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

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