# Q: 5  Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Given : ABCD is a quadrilateral with  AC=BD,AO=CO,BO=DO,COD =

To prove: ABCD is a square.

Proof: Since the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a rhombus.

Thus, AB=BC=CD=DA

AB=AB               (common)

BD=AC

(CPCT)

2. ABC =

ABC =

Hence,  the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

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