Question 1186189
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The figure is a trapezoid in which line m is perpendicular to both bases and bisects both of them.<br>
The proofs for the two cases should be nearly identical.  In both cases, AC is the hypotenuse of a right triangle; one leg is along the longer base of the trapezoid and the length of the other leg is the distance between the two bases of the trapezoid.<br>
In one case the length of the base of the triangle is half the longer base minus half the shorter base; in the other case it is half the longer base plus half the shorter base.<br>