Question

If the diagonals of a parallelogram
equal then show that
it is a rectangle

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Answer 1

Answer:

Hope this helps u

Answer 2

$\huge \mathcal \colorbox{black}{{ \color{cyan}{Solution:-}}}$

A parallelogram ABCD in which AC=BD

To prove:-ABCD is a rectangle.

Proof:-In∆s ABC and DCB,we have

• AB=DC
• BC=DA
• AC=DB

∴By SSS criterion of congruence

∆ ABC≌∆ DCB

∠ ABC =∠ DCB

[Corresponding parts of congruent triangles are equal]

But AB ∥ DC and BC cuts them.

∴ ∠ABCD +∠DCB=180°

2ABC=180°

[Sum of consecutive interior angles is 180°]

∠ABC=90°

Thus,∠ABC=∠DCB=90°

⤏ABCD is a parallelogram one of whose angle is 90°.Hence,ABCD is a rectangle.