Problem
GEO-B1-M07-P005 Reflect a Point About a Midpoint
#5
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Point \(M\) is the midpoint of \(BC\). Point \(D\) is the reflection of \(A\) about \(M\). Prove that the diagonals of quadrilateral \(ABDC\) bisect each other.
Which two segments are bisected by point \(M\)?
Since \(M\) is the midpoint of \(BC\), \(BM=MC\). Since \(D\) is the reflection of \(A\) about \(M\), \(AM=MD\). Thus point \(M\) bisects diagonals \(BC\) and \(AD\) of quadrilateral \(ABDC\).
Reflection about a midpoint is almost the same as extending a segment by an equal length.