This investigation is a great demonstration to help students visualize similar right triangles!

To begin, start with a regular sheet of paper. Then, draw a diagonal across the page from one corner to another. This creates two congruent right triangles. Then, fold the paper to find the altitude to the hypotenuse of one of the triangles. Remember, the altitude is perpendicular.

Along the fold, outline the triangles and draw the altitude.

Now, have students point out the congruent angles. It might be helpful if you label the points with letters. Remind students of the triangle congruence theorems. Since all of the angles are congruent, can you prove the triangles are congruent?

Cut the triangles apart. Arrange them so that they are facing the same direction. When this is done, it is easy to see that the triangles are similar.

Stack the triangles so that the three congruent acute angles match up. This also helps show that the triangles are similar.

After I do this demonstration, I like to use my Similar Right Triangles foldable. When students have trouble, I remind them of the demonstration and have them draw the triangles separately. This demonstration could even be "souped up" and used as the actual lesson.