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Please help me prove that A parallelogram is a rectangle if and only if its diagonals are congruent, and in that case the diagonals bisect each other.

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00:38

Prove: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

01:45

Prove that the diagonals of any parallelogram bisect each other.

03:36

Prove that the diagonals of a rectangle are congruent.

01:14

Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in length.

Transcript

Hello students. So in this question we have to show that a parallelogram is a rectangle. If and only if it’s diagonals are congruent. So we have a parallelogram. A B C. D. Abc lee is a parallelogram. So we have to prove that it is a rectangle effort diagnosed are equal on weekends. We are going to prove it in a reverse way. That is let us assume dr A C. Is request to beauty. We’re already assuming assuming that diagonals are congruent. Now if we prove that anyone of this angle is 90° then it will be a rectangle. So we have to prove that every diagnosis required then this parallelogram is a rectangle. Then obviously the converts will also be true that if the parallelogram is a rectangle if diagnosed will be congruent. So we are assuming that request ability. So we know that in a parallelogram opposite sides are equal. That means this baby will be question authority and this lady will be questioned. B. C. This is the property of the parallelogram, opposite sides are equal and as well as they are parallel. Okay, now we have entangled and triangle abc undo. Rangel, B C. B. What is the triangle abc? This triangle? This is our abc triangle A. B. C. On triangle Dcb PCBs are this triangle dcB Okay, so in these two triangles we know that A B is in question. Dc A B is a question busy. This is the property of a parallelogram oppositions are equal. So I’m not writing it then we have B. C. As a common side. So busy will be questioned busy as the side is common, then we have a C. Is the question ability but we have assumed yes we have. I assume that means strangled. Abc is…

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