Construct exterior squares on the sides of a triangle. Then GQ is congruent and perpendicular to AL.

Drag A.

Compare the velocity of point G with the velocity of Q.

CA is sqrt 2 CG, rotated 45o. Therefore the velocity of A is sqrt 2 the velocity of G, rotated 45o. BA is sqrt 2 BQ rotated 45o the other way. Therefore the velocities of G and Q are rotated 90o and have the same magnitude. Therefore LA is equal to GQ rotated 90o plus a constant. To see that the constant is zero, let A coincide with C.

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Three squares on a triangle
Figure 11

Alfinio Flores
ASU

This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1997 by Key Curriculum Press, Inc. All rights reserved. Portions of this work are being funded by the National Science Foundation (awards DMI 9561674 & 9623018).