How Do We Use Right Triangles similarity?

In Figure 1 , right triangle ABC has altitude BD drawn to the hypotenuse AC. 

Figure 1 An altitude drawn to the hypotenuse of a right triangle.

The altitude drawn to the hypotenuse of a right triangle creates two similar right triangles, each similar to the original right triangle and similar to each other.

Figure 2 shows the three right triangles created in Figure 1 . They have been drawn in such a way that corresponding parts are easily recognized. 

Figure 2 Three similar right triangles from Figure 1 (not drawn to scale).

AB and BC are legs of the original right triangle; AC is the hypotenuse in the original right triangle; BD is the altitude drawn to the hypotenuse; AD is the segment on the hypotenuse touching leg AB and DC is the segment on the hypotenuse touching leg BC. Because the triangles are similar to one another, ratios of all pairs of corresponding sides are equal. This produces three proportions which are 

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