Pythagorean Theorem on Hinges with Equilateral Triangles

####Pythagorean Theorem, Equilateral Triangles, Math Puzzles

Can an equilateral triangle be dissected and turned around on the hinges into two equilateral triangles? How about the other way around?

The Pythagorean Theorem is typically introduced using squares on the three sides of a right triangle. It is fine! However, we don’t have to use squares. Any similar 2D shapes constructed on the three sides of the right triangle will do the job for establishing the Pythagorean Theorem. Equilateral triangles (and semicircles) are quite interesting shapes to use in K-12 math classes. The present design uses equilateral triangles with three hinges to demonstrate the fact that a 3-equilateral triangle and a 4-equilateral triangle can be assembled into a 5-3-equilateral triangle. One can use two sets of equilateral triangles to show the relationship.

In essence, we are using 1-equilateral triangles to measure areas. The bottom line is that all equilateral (and all semicircles) are similar to each other. This design also works like a math puzzle without mentioning the Pythagorean Theorem.

####Among the Files
1. Right triangle plus a set of equilateral triangles
2. One set of equilateral triangles without the right triangle

Have fun playing with math ideas!

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