4.2.3 Triangle Congruence: CPCTC (continued) Example 4 Using CPCTC in a Coordinate Proof
CPCTC can be used in a coordinate proof just as it was used in other proofs. First show that the two triangles are congruent, then use CPCTC to show that some pair of corresponding parts are congruent. Remember, when given a figure on a coordinate plane, the lengths of the figure’s sides can always be determined by using the distance formula. For this proof, first find the length of each side of △ ABC and of △ DEF by using the distance formula. Then, since DF = AC , EF = BC , and DE = AB , the two triangles are congruent by SSS. So, since ∠ BCA and ∠ DFE are corresponding angles, ∠ BCA ≅ ∠ DFE by CPCTC.
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