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Question 1186189: Line m is the perpendicular bisector of both AB and CD. Which of the following must be true and why (or why not)?
AC=BD
(I know it is true and I have proved AC=BD when A and C are both on one side, but there is also a possibility with different triangles, where C is on the opposite side of A. How do I prove that? Thank you.)
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The figure is a trapezoid in which line m is perpendicular to both bases and bisects both of them.
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.
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.
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