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Mathematics

ABCD is a rectangle in which diagonal BD bisects ∠B. Can we definitely say that ABCD is a square?

Rectilinear Figures

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ABCD is a rectangle in which diagonal BD bisects ∠B. Can we definitely say that ABCD is a square? Quadrilaterals, R.S. Aggarwal Mathematics Solutions ICSE Class 9.

In a rectangle, all angles are 90°.

Given that diagonal bisects ∠B

∠ABD = ∠DBC = 45°

This implies that the diagonal makes equal angles with sides BA and BC, which can happen only if AB = BC.

A rectangle with adjacent sides equal is a square.

Yes, ABCD is a square.

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