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Pythagorean Analogs for Similar Triangles

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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.

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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.

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Contributed by: S. M. Blinder (March 2011)
Open content licensed under CC BY-NC-SA

Snapshots

Details

Snapshot 1: three equilateral triangles

Snapshot 2: an "inside job"

Snapshot 3: something more bizarre. The Pythagorean relation is still valid!

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