Question

show that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus

Answer 1

it's rough diagram.....

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Answer 2

Answer:

Hi mate here is the answer:--✍️✍️

Question:-✔️✔️

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Solution:-✔️✔️

To Prove:

If diagonals of a quadrilateral bisect at 90º, it is a rhombus.

Definition of Rhombus:

A parallelogram whose all sides are equal.

Given:

Let ABCD be a quadrilateral whose diagonals bisect at 90º.

In ΔAOD and ΔCOD,

In ΔAOD and ΔCOD,OA = OC (Diagonals bisect each other)

In ΔAOD and ΔCOD,OA = OC (Diagonals bisect each other)∠AOD = ∠COD (Given)

In ΔAOD and ΔCOD,OA = OC (Diagonals bisect each other)∠AOD = ∠COD (Given)OD = OD (Common)

∆AOD congruent ∆ ΔCOD (By SAS congruence rule)

AD = CD ..................(1)

Similarly,

AD = AB and CD = BC ..................(2)

From equations (1) and (2),

AB = BC = CD = AD

Since opposite sides of quadrilateral

ABCD are equal, it can be said that ABCD is a parallelogram. Since all sides of a parallelogram ABCD are equal, it can be said that

ABCD is a rhombus

Hence, Proved.

Hope it helps you ❣️☑️☑️

Step-by-step explanation: