# Parallelogram Law: A PWW

Parallelogram Law asserts that the sum of squares formed on the diagonals of a parallelogram equals the sum of squares formed on its sides. The applet is a realization of an idea first conceived by Douglas Rogers. A heptagon that appears in a proof of the Law of Cosines is naturally expanded to an octagon with a four-fold rotational symmetry. The octagon is decomposed in four ways which combine to suggest a proof (without words) of the parallelogram law.

(The blue parallelogram in the upper left corner and its vertices are draggable.)

What if applet does not run? |

The octagon, with its decompositions, emerges in a related plane tessellation.

### Proofs Without Words

- Proofs Without Words
- Sums of Geometric Series - Proofs Without Words
- Sine of the Sum Formula
- Parallelogram Law: A PWW
- Parallelogram Law
- Ceva's Theorem: Proof Without Words
- Viviani's Theorem
- A Property of Rhombi
- Triangular Numbers in a Square
- PWW: How Geometry Helps Algebra
- Varignon's Theorem, Proof Without Words

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

Copyright © 1996-2018 Alexander Bogomolny

68361753