Question

At which angle do diagonals of a rhombus bisects each other?

(a) 180°

(b) 360°

(c) 270°

(d) 90°

This question was addressed to me in homework.

Question is from Types of Quadrilaterals in chapter Quadrilaterals of Mathematics – Class 9

Answer 1

Right option is (d) 90°

The best explanation: A rhombus is shown in the diagram below.

For ∆AOB and ∆AOD,

AB = AD (sides of the same rhombus)

OB = OD (diagonals of a parallelogram bisect each other)

OA = OA (same side)

Hence, according to SSS rule, ∆AOB and ∆AOD are congruent to each other.

Therefore,

∠AOB = ∠AOD

∠AOB + ∠AOD = 180° (linear pair of angles)

2∠AOD = 180°

Therefore, ∠AOD = 90°