Three similar triangles
- Judah L Schwartz
The large GRAY right triangle is cut into the GREEN and BLUE triangles. [You can vary the right triangle by dragging the white dots. You can translate the green and blue triangles by dragging the yellow dots. You can rotate the green and blue triangle by dragging the yellow rings.] The GRAY, GREEN and BLUE triangles are similar to one another. The ratio of the lengths of corresponding segments in the BLUE and GRAY triangles as well as the ratio of the lengths of corresponding segments in the GREEN and GRAY triangles are shown. Can you formulate a scaling argument to prove the Pythagorean Theorem?