Question

ramu said that in a rhombus the diagonals bisect each other perpendicular . do you agree with him.​

Answer 1

Yes , in a rhombus diagonals bisect each other.

★ ANSWER

The opposite sides of a parallelogram are equal, so if two adjacent sides are equal, then all four sides are equal and it is a rhombus.

★ Theorem

If two adjacent sides of a parallelogram are equal, then it is a rhombus.

A quadrilateral whose diagonals bisect each otherat right angles

★ Theorem

A quadrilateral whose diagonals bisect each other at right angles is a rhombus.

★ Proof

Let ABCD be a quadrilateral whose diagonals bisect

each other at right angles at M.

We prove that DA = AB. It follows similarly that

AB = BC and BC = CD

triangleAMB equiv triangleAMD (SAS)

So AB = AD and by the first test above ABCD is a rhombus.

A quadrilateral whose diagonals bisect each other is a parallelogram, so this test is often stated as

‘If the diagonals of a parallelogram are perpendicular, then it is a rhombus.’

Answer 2

Answer:

Here is your answer

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