Folding Triangles to Rectangles

####Folding Triangles to Rectangles

A triangle can be folded physically or mentally to a rectangle, as shown in the pictures, using two side midpoints and some lines as references. This is one way to justify the area of triangle is 1/2 * base * height or rather two rectangles, each of which has a length of 1/2 of the triangle base and a width of 1/2 of the triangle height.

The 3D models show the ideas but cannot be readily flattened without breaking the pieces off. Yes, one can break them apart and then reassemble them. Alternatively, one can mentally fill the gap or resort to paper models. **Challenge**: Why does it work?

#### Among the Files

1. An equilateral triangle
2. Two right triangles
3. Just another triangle