Prove that bisectors of any two adjacent angles of a parallelogram are at right angles
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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°.
Hope it's helpful to u.
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°.
Hope it's helpful to u.
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