Use coordinates to prove simple geometric theorems, including simple circle theorems.
Complete a coordinate proof from calculated evidence
Problem
The distinct nonvertical supporting lines of \(AB\) and \(CD\) \(\text{both}\) have calculated slope \(2\). State the coordinate theorem connecting this evidence to the line relationship and complete the proof conclusion.
Big Picture
What this problem is really about
A coordinate proof is complete only when the calculated evidence is connected to a theorem with every hypothesis checked. We’ll interpret the two slopes as directions, confirm the lines are finite-slope and distinct, apply the matching line theorem, and state the exact supporting-line conclusion without confusing direction with segment length.
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