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Using Congruent Triangles to Prove Relationships in a Diagram

Learn how to use congruent triangles to prove relationships in a diagram by applying specific angle and side information. Examples and solutions included.

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Using Congruent Triangles to Prove Relationships in a Diagram

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  1. GIVEN ∠ RTQ RTS 1 2, QTST PROVE If you can show that QRT SRT, you will know that QT ST. First, copy the diagram and mark the given information. EXAMPLE 1 Use congruent triangles Explain how you can use the given information to prove that the hanglider parts are congruent. SOLUTION

  2. Mark given information. Add deduced information. Two angle pairs and a non-included side are congruent, so by the AAS Congruence Theorem, . Because corresponding parts of congruent triangles are congruent, QRT SRT QTST. EXAMPLE 1 Use congruent triangles Then add the information that you can deduce. In this case, RQT and RST are supplementary to congruent angles, so ∠ RQT RST. Also, RTRT .

  3. Explain how you can prove that AC. AB BC Given AD DC Given BD BD Reflexive property ANSWER Thus the triangle by SSS ABDBCD for Example 1 GUIDED PRACTICE SOLUTION

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