Proving That a Parallelogram is a Rectangle
Given a parallelogram with congruent diagonals, you are asked to prove that the parallelogram is a rectangle. Would saying:
A parallelogram must be a rectangle if the diagonals are congruent.
be a valid proof for this question?
$\endgroup$ 12 Answers
$\begingroup$If you have already proven this theorem, you can reference it and it is a fine proof. If you have not already proven it, you need to do so. By cutting the parallelogram into four triangles by the diagonals and showing that the triangles are congruent if the diagonals are, you can get there. There are other approaches as well.
$\endgroup$ 1 $\begingroup$It is valid if you can prove your claim. Here is a hint on how to prove it:
$\endgroup$Assuming your definition of a parallelogram is that it is a convex quadrilateral in which two opposing sides are congruent, then you can use the SSS (side-side-side) criterion for congruency of triangles, together with angle sum of convex quadrilaterals
