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smc

geometry senior

Problem

Let be a quadrilateral with extended to so that . Lines and are drawn to form . For this angle to be a right angle it is necessary that quadrilateral have:
(A)
(B)
(C)
(D)
Solution
Because is right, the midpoint of its hypoteneuse (namely, ) is its orthocenter. Thus, , and so two side lengths of quadrilateral are equal. The placement of is irrelevant. Thus, our answer is .
Final answer
D