Below you can see two right triangles, a red one AB'C' and a blue one ABC. Since both triangles have the same angle α the triangles are similar. (the the second angle is a right angle and the third angle γ=180°-α-90°).
The theorem of proportional segments states that in similar triangles the ratios of two respective sides are always equal.

1. Move the vertices A and B and notice the ratio of opposite leg and hypothenuse. The worksheet shows that both triangles always have the same value of the ratio of opposite leg and hypothenuse.
2. If you move B horizontally, the angle α does not change. You can see that the ratio of opposite leg and hypothenuse remains the same.