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Consider triangles and below. Give a convincing argument that . Then use what you know about similar triangles to complete each of the following ratios for the triangles shown below.

Right triangle, A, C, B, has horizontal leg, A, C, labeled, x, and vertical leg, C, b, labeled, y. The horizontal leg is extended, past the right angle, creating a larger right triangle, A, E, D, with horizontal leg, A, E, labeled, m, and vertical leg, E, d, labeled, n.


    Notice that and are the longer and shorter legs of .

    Remember that and are similar, which means their sides are proportional.


    Notice that both and are the short legs in both triangles.