How to Prove a Quadrilateral Is a Parallelogram

The Organic Chemistry Tutor

This comprehensive math tutorial guides students through the logical process of proving that a quadrilateral is a parallelogram using formal geometric proofs. The video begins by outlining five fundamental methods for proving a figure is a parallelogram, including showing opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, or diagonals bisect each other. This theoretical foundation sets the stage for applying specific geometric postulates like SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and CPCTC (Corresponding Parts of Congruent Triangles are Congruent). The core of the video focuses on walking through three distinct, step-by-step examples using two-column proofs. The instructor demonstrates how to translate visual geometric diagrams and given statements into a structured logical argument. By creating statements and providing valid reasons for each step, the video models the exact thinking process required in high school geometry. Topics include midpoint definitions, vertical angles, and segment addition postulates. For educators, this video serves as an excellent modeling tool for teaching two-column proofs, a historically difficult concept for many students. It moves beyond simple calculation to deep conceptual understanding of geometric properties and deductive reasoning. Teachers can use the specific examples to scaffold learning, starting with identifying properties and moving toward constructing full proofs independently.