Advanced CPCTC Problems and Solutions

This final page presents three challenging CPCTC proof problems, demonstrating advanced applications of the concept.

Problem 1 involves proving angle congruence when a point is the midpoint of a line segment and two other segments are congruent. The solution uses the SSS theorem and CPCTC.

Problem 2 requires proving side congruence in a quadrilateral with parallel sides. This proof combines alternate interior angles, the ASA theorem, and CPCTC.

Problem 3 involves parallel lines and congruent angles. The solution uses the ASA theorem and CPCTC to prove angle congruence.

Highlight: These problems showcase how CPCTC can be used in conjunction with various geometric concepts like parallel lines, midpoints, and different triangle congruence theorems.

Tip: When solving complex CPCTC problems, break down the proof into smaller steps and identify which congruence theorem to use before applying CPCTC.

Advanced Applications of CPCTC

This page presents three more sophisticated examples of CPCTC proofs, showcasing its versatility in solving complex geometric problems.

Example 1 involves proving angle congruence when a point is the midpoint of two line segments. The proof uses the ASA (Angle-Side-Angle) theorem and CPCTC.

Example 2 demonstrates how to prove that an angle bisector creates two congruent segments. This proof also utilizes the ASA theorem before applying CPCTC.

Vocabulary: Angle bisector - a line that divides an angle into two equal parts.

Example 3 is a more complex proof involving parallel lines and midpoints. It uses the AAS theorem and CPCTC to prove segment congruence.

Highlight: These examples show how CPCTC can be combined with various triangle congruence theorems to solve diverse geometric problems.