Orthogonality in Two Squares
What Is This About?
Problem
$AMNP$ and $ABCD$ are two squares.
Prove that $BM\perp DP.$
Solution
Observe that the counterclockwise (in the diagram below) rotation through $90^{\circ}$ around point $A$ brings $P$ to $M$ and $D$ to $B.$
Thus, the entire $\Delta ADP$ maps onto $\Delta ABM,$ implying, in particular, that their third sides are also perpendicular: $BM\perp DP.$
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