10176

# Pythagorean Analogs for Similar Triangles

An analog of Pythagoras' theorem is satisfied for three similar polygons of any shape constructed on the sides of a right triangle. In this Demonstration, this is illustrated with three similar triangles colored red, blue, and green. The area of the red triangle equals the sum of the areas of the blue and green triangles.
Drag the locator to vary the shape of the red triangle. The blue and green triangles will automatically synchronize to maintain similarity.
The Pythagorean relationship remains valid if the colored triangles are moved inside the right triangle and even in bizarre configurations with the locator moved through the right triangle.

### DETAILS

Snapshot 1: three equilateral triangles
Snapshot 2: an "inside job"
Snapshot 3: something more bizarre. The Pythagorean relation is still valid!

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.