Answer: CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." A theorem in geometry states that if two triangles are congruent, their corresponding parts (sides and angles) are also congruent.
To provide a proof involving CPCTC, let's consider the following scenario:
Given: Triangle ABC is congruent to Triangle DEF
To Prove: Angle A is congruent to Angle D
Proof:
1. Triangle ABC is congruent to Triangle DEF (Given)
2. Corresponding parts of congruent triangles are congruent (CPCTC)
3. Angle A corresponds to Angle D in the congruent triangles (Definition of corresponding angles)
4. Therefore, Angle A is congruent to Angle D (Conclusion from CPCTC and corresponding angles)
In this proof, we start with the given information that Triangle ABC is congruent to Triangle DEF. Then, we apply the CPCTC theorem, which tells us that the corresponding parts of congruent triangles are congruent. Since we are specifically interested in the angles, we focus on Angle A and Angle D. By the definition of corresponding angles, we can conclude that Angle A is congruent to Angle D.
This proof demonstrates the use of CPCTC to establish the congruence of angles in congruent triangles.
Explanation: