I am working through Serge Lang's book on geometry, and I am having trouble for some reason on this proof:
Given that AC is on the perpendicular bisector of BD, and that BD lies on the perpendicular bisector of AC. Prove that quadrilateral ABCD is a rhombus (a rhombus is a parallelogram whose four sides have the same length).
It is easy to prove that the four sides are of equal length, but I don't know how to prove that the pairs of sides are parallel. I think I should prove that the interior angles are supplementary, but I'm not sure how to do that. Any tips?
Given that AC is on the perpendicular bisector of BD, and that BD lies on the perpendicular bisector of AC. Prove that quadrilateral ABCD is a rhombus (a rhombus is a parallelogram whose four sides have the same length).
It is easy to prove that the four sides are of equal length, but I don't know how to prove that the pairs of sides are parallel. I think I should prove that the interior angles are supplementary, but I'm not sure how to do that. Any tips?
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