Question

prove that the diagonals of a rhombus bisect each other at right angles


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Answer 1

✪ Question ✪

Prove that the diagonals of a rhombus bisect each other at right angles.

✪ To prove ✪

The diagonals of a rhombus bisect each other at right angles.

✪ Proof ✪

Let ABCD be a rhombus whose diagonals AC and BD Intersect at the point O.

We know that the diagonals of a parallelogram bisect each other.

Also, we know that every rhombus is a parallelogram.

So, the diagonals of a rhombus bisect each other.

∴ OA = OC and OB = OD

From ∆COB and ∆COD, we have:

CB = CD (sides of a rhombus)

CO = CO (common)

OB = OD (proved above)

∴ ∆COB ≅ ∆COD (by SSS congruence)

↝∠COB = ∠COD

But, ∠COB + ∠COD = 2 right angles (linear pair)

∴ ∠COB = ∠COD = 1 right angle

Hence, the diagonals of a rhombus bisect each other at right angles.

✪ Proved ✪

The diagonals of a rhombus bisect each other at right angles.

๑ Hope this helps you. ๑