artofproblemsolving.com
https://artofproblemsolving.com/wiki/index.php?tit…
Art of Problem Solving
Problem In the figure, is a square of side length . The rectangles and are congruent. What is ? Solution 1 Draw the altitude from to and call the foot . Then . Consider . It is the hypotenuse of both right triangles and , and we know , so we must have by Hypotenuse-Leg congruence. From this congruence we have . Notice that all four triangles in this picture are similar. Also, we have . So set ...
