How to Use CPCTC in Geometry Proofs

The Organic Chemistry Tutor

This comprehensive geometry tutorial provides a step-by-step guide to using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) in two-column proofs. The video begins by reviewing the four primary postulates for proving triangle congruence: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS). It then logically transitions into explaining how CPCTC allows students to prove that specific sides or angles are congruent once the triangles themselves have been proven congruent. The core of the video consists of seven distinct practice problems that increase in complexity. These examples cover a wide range of geometric concepts, including perpendicular lines, midpoints, circle radii, vertical angles, parallel lines, alternate interior angles, and angle bisectors. By incorporating these varied elements, the video demonstrates how to synthesize different geometric definitions and theorems to construct a complete proof. For educators, this video serves as an excellent resource for modeling the logical flow of formal proofs. It emphasizes the importance of justifying each step with a specific reason, definition, or property (such as the Reflexive Property or Segment Addition). The clear, paced explanations and visual markings on the diagrams help students visualize the relationships between geometric parts, making abstract proof concepts more accessible and concrete.