Question

show that if diagonal of quadrilateral bisect each other at right angle,then it a rhombus.​

Answer 1

Answer:

Let ABCD be a quadrilateral whose diagonals bisect each other at right angles.

Given,

OA = OC, OB = OD and ∠AOB = ∠BOC = ∠OCD = ∠ODA = 90°

To show,

ABCD is parallelogram and AB = BC = CD = AD

Proof,

In ΔAOB and ΔCOB,

OA = OC (Given)

∠AOB = ∠COB (Opposite sides of a parallelogram are equal)

OB = OB (Common)

Therefore, ΔAOB ≅ ΔCOB by SAS congruence condition.

Thus, AB = BC (by CPCT)

Similarly we can prove,

AB = BC = CD = AD

Opposites sides of a quadrilateral are equal hence

ABCD is a parallelogram.

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Thus, ABCD is rhombus as it is a parallelogram whose diagonals intersect at right angle.

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Answer 2

Answer:it may be helpful to you.....

Step-by-step explanation:

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