Question

Prove that bisectors of any two adjacent angles of a parallelogram are at right angles

Answer 1

Assume ABCD is a parallelogram.

Bisectors of A and B meet at O.

To proof Angle AOB = 90°

Since Sum of Angle A and B = 180°

=) Sum of bisectors of both angle = 180°/2 = 90°

In triangle AOB;

Angle OBA + Angle OAB + Angle AOB = 180°

=) 90°+ Angle AOB = 180°

=) Angle AOB = 90°.

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