Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.
Find missing side lengths using the triangle midsegment theorem
Problem
In triangle \(ABC\), the tick marks show that \(M\) and \(N\) are the midpoints of \(AC\) and \(BC\). Segment \(MN\) is parallel to \(AB\) and \(MN=8\). Find \(AB\).
The key is deciding which segment is the half-length: the midpoint connector is half the third side, not equal to it. We’ll verify both endpoint midpoint marks, pair the connector with the parallel base, then reverse the one-half relationship and check by halving the recovered whole.
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