4.2.3 Triangle Congruence: CPCTC (continued) Example 2 Proving Corresponding Parts Congruent
A flowchart proof is used in this example to prove that two sides are congruent. Remember, CPCTC can be used to prove the congruence of a pair of corresponding sides (or angles) in two triangles, but only after the two triangles are shown to be congruent. So, the first task in this proof is to show that △ AEB ≅ △ CED . Two pairs of congruent sides are given. Additionally, their included angles are congruent by the Vertical Angles Theorem (since ∠ AEB and ∠ CED are vertical angles). So, the two triangles must be congruent by SAS. Now, since △ AEB ≅ △ CED by SAS, any of their corresponding parts can be shown to be congruent by CPCTC.
Example 3 Using CPCTC in a Proof
In this proof there are two pieces of given information.
1. Y is the midpoint of XZ . 2. ∠ XYW is a right angle.
Notice that the angles to prove congruent, ∠ XWY and ∠ ZWY , are corresponding angles in △ XWY and △ ZWY . Therefore, first show that △ XWY ≅ △ ZWY and then use CPCTC to show that ∠ XWY ≅ ∠ ZWY .
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