Use coordinates to prove simple geometric theorems, including simple circle theorems.
Choose the coordinate method needed for a proof goal
Problem
A coordinate proof must establish that \(\text{two}~\text{segments}\) are congruent. Name the direct coordinate method and state the equality that its results must satisfy.
Big Picture
What this problem is really about
The proof goal determines the coordinate tool: segment congruence asks for equal lengths, not equal directions or shared midpoints. We’ll translate the goal into a length equality, write the endpoint-distance expressions for both segments, compare their squared forms exactly, and connect that equality back to congruence.
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