Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Test the diagonal-bisection converse for a parallelogram
Problem
Decide whether the diagonal evidence is sufficient to prove a parallelogram: quadrilateral \(ABCD\); diagonals \(AC\) and \(BD\) intersect at \(M\) and are stated to bisect each other.
The diagonal converse needs mutual bisection: the same intersection must be the midpoint of both diagonals. We’ll trace each diagonal through the shared point, verify its own two halves are equal, and apply the converse only after both midpoint relationships are established.
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