How to Solve Two-Column Proofs for Quadrilaterals

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on constructing two-column geometric proofs involving four specific types of quadrilaterals: parallelograms, isosceles trapezoids, rhombuses, and kites. The narrator systematically guides viewers through four distinct examples, demonstrating how to use the given information (the properties of the shape) to prove that specific line segments within the figures are congruent. The video emphasizes the use of triangle congruence theorems such as AAS (Angle-Angle-Side), ASA (Angle-Side-Angle), and SAS (Side-Angle-Side), as well as the CPCTC principle (Corresponding Parts of Congruent Triangles are Congruent). The central themes explored include the specific properties of quadrilaterals (e.g., opposite sides of a parallelogram are parallel, base angles of an isosceles trapezoid are congruent, diagonals of a rhombus bisect angles) and the application of logic to build a valid mathematical argument. The video also reviews foundational geometric concepts like vertical angles, alternate interior angles formed by parallel lines, and the reflexive property of congruence. For educators, this video serves as an excellent modeling tool for high school geometry classrooms. It bridges the gap between learning the properties of shapes and applying them in formal proofs, a common struggle for students. Teachers can use the individual examples as direct instruction segments, pausing to let students predict the next step or the reason for a statement. It is particularly useful for reinforcing how to identify congruent triangles hidden within quadrilaterals to prove properties about diagonals and segments.