Use precise definitions of angle, circle, perpendicular line, parallel line, and line segment from point/line/distance ideas.
Write a precise definition for perpendicular lines
Problem
Use the displayed example and nonexample to define perpendicular lines precisely, state the consequence for all \(\text{four}\) angles at the intersection, and explain why the nonexample fails.
An example–nonexample pair helps isolate the condition that actually changes the classification. We’ll compare the marked angle with the measured acute angle, express the decisive condition as an if-and-only-if statement, and then use vertical angles plus linear pairs to account for every angle around the intersection.
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