How to Write Two-Column Proofs with Medians and Altitudes

The Organic Chemistry Tutor

This educational video provides a detailed tutorial on writing two-column proofs in high school geometry, specifically focusing on triangles involving medians and altitudes. The narrator guides viewers through two distinct problems, demonstrating how to logically structure arguments using statements and reasons. The first problem proves the congruence of exterior base angles in an isosceles-like setup using medians, while the second problem proves a line segment is a median given that it is an altitude and an angle bisector. The content explores fundamental geometry concepts including the definitions of medians and altitudes, the reflexive property of congruence, triangle congruence postulates (SSS and ASA), and the principle of CPCTC (Corresponding Parts of Congruent Triangles are Congruent). It also touches on supplementary angles and linear pairs. The step-by-step approach models the rigorous thinking required for mathematical proofs, showing students how to translate given information into a logical sequence of deductions. This video is highly valuable for geometry teachers and students as a resource for mastering the difficult skill of writing formal proofs. It breaks down the often-intimidating two-column format into manageable steps, explaining the "why" behind each move. It serves as an excellent model for classroom instruction, allowing teachers to pause and let students predict the next logical step, or as a review tool for students struggling with the mechanics of geometric reasoning.