We know that two triangles are similar if they meet the Angle-Angle Triangle Similarity Theorem criteria. One way to create triangles with congruent angles is to use reflection. When light bounces off a mirror or a ball bounces off a hard surface, the angle at which it hits is the same as the angle at which it returns. In one-wall handball people bounce a ball off a wall and try to aim for a spot from which their opponent won't be able to return the ball.

Rectangle with horizontal line B C on top, point E plotted. Right side of rectangle, Point A near middle. Horizontal line from point A across rectangle. Left side of rectangle, point D near lower left corner. A B labeled 16. A to tick mark below labeled 9. Tick mark to bottom of rectangle labeled 9. Bottom of rectangle labeled 20. Bottom to point D labeled 2. Dotted diagonal line segments A E and E D drawn, angles B E A and C E D marked congruent.

Where on the wall should we aim if we're standing at point and want the ball to land at point ? We know the triangles are similar because of the Angle-Angle Triangle Similarity Theorem. Segment corresponds to segment . So the scale factor to go from triangle to triangle  is . Segments and also correspond so they must have the same scale factor. Because  , segments and must be in a ratio. Dividing the 20 foot wall into 3 equal parts tells us that . In practice it's easier to think about aiming for a third of the way along the wall from the right-hand side than it is to aim for a spot feet away from point .