Flowchart Proofs

Geometry · Axiom Academy

Visualizing the logical flow of a geometric argument — boxes for statements, arrows for the reasoning that connects them, built straight from the figure. Every flowchart proof reads from the top down . The given facts sit at the top, each deduction gets its own box, and the conclusion lands at the bottom — an arrow means "this follows from the box before it." Play it once: the boxes appear in logical order while the matching part of the figure lights up. The facts you're handed sit at the top — every other box has to trace back to them. Each statement is about a specific part of the diagram, so the picture and the logic move together. An arrow into a box means that box is forced by the one the arrow came from. The statement you set out to prove is the last box every chain flows into. 2. Example: A Linear Pair Is Supplementary When two angles form a linear pair , their non-shared sides form a straight line. Watch the chain build one box at a time — and watch each piece of the angle figure light up as its statement is justified. The opposite rays and make a straight angle, so by the Angle Addition Postulate . Two angles whose measures sum to are supplementary by definition — which is exactly what we set out to prove. 3. A Branching Proof: Congruent Supplements

This is the written version of the interactive lesson above. See the full Geometry course.