Students will learn what the hypotenuse-angle theorem is, why it's true, and how to use it.

Hypotenuse Angle (HA) | Theorem by MATEMATIKA

Conclude by giving your students these challenges:

The three angles pictured below are equal. Mentally determine the fraction that's shaded.

Here's the answer.

What angle is made by the two red lines drawn on the two sides of the cube, as shown in the illustration?

Solution: If the ends of the two red lines at the bottom left and top left are connected by a third red line along the invisible left face of the cube, then since each of the red lines joins two opposite corners of same-sizes squares, those three lines form an equilateral triangle. Hence at each corner of that triangle, two red lines meet at 60 degrees.

Note: This is a puzzle printed by Martin Gardner. I'm not sure if he's the creator and I'm not sure which Gardner book this puzzle appears in.