Monday I asked my students to determine whether this triangle was equilateral, isosceles, or scalene, and to prove their answer. The hint is in the post title: this is a Pythagorean Theorem activity. Here is the original triangle:
If you said “isosceles,” you’re correct! Here’s the proof, using Pythagoras’s Theorem.
The hypotenuse of the right triangle, shown in red, is 5 units — the same as the base of the original triangle. Therefore the triangle has two congruent sides and is isosceles!