Orthogonality in Two Squares

What Is This About?

21 October 2015, Created with GeoGebra

Problem

$AMNP$ and $ABCD$ are two squares.

Orthogonality in Two Squares - problem

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 $B.$

Orthogonality in Two Squares - solution

Thus, the entire $\Delta ADP$ maps onto $\Delta ABM,$ implying, in particular, that their third sides are also perpendicular: $BM\perp DP.$

|Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2017 Alexander Bogomolny

 62618655

Search by google: