The
PYTHAGOREAN SIMILAR RECTANGLES
Problem
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The
PYTHAGOREAN SIMILAR RECTANGLES
Problem
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Given:
In the figure above on the left the triangle is any right triangle with an
arbitrary point selected on the hypotenuse, creating two segments, x and y, on the hypotenuse.
From this point perpendicular lines are drawn to each of the legs, creating segments a, b, m, and n
on the legs. The total of six segments will form 3 rectangles, I, II, and III as shown in the
figure on the right.
Show: algebraically that the sum of the areas of the two smaller rectangles, I and II, in
the figure above on the right is equal to the area of the larger rectangle, III.
That is, show:
