Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Test both perpendicular-bisector conditions
Problem
Classify the candidate line using only the perpendicular-bisector definition: line \(\ell~\) passes through \(M\), \(M\) is the midpoint of \(AB\), and \(\ell~\perp~AB\).
The name perpendicular bisector contains two independent tests, and neither one alone is enough. We’ll check that the candidate line passes through the segment’s midpoint, separately check that it forms a right angle with the segment, and classify it only after both conditions are confirmed.
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