Question

Prove that Bisectors of
any 2 consecutive
angles of a parallelogran
intersect at Right angles.​

Answer 1

let the angles be A an B

sum of consecutive angles of a parallelogram is 180 degree

∠A + ∠B =180°

by drawing bisectors

1/2×∠A + 1/2×∠B =1/2×180

Let the two bisectors meet at O

therefore

∠OAB+∠OBA=90°-----------(1)

In triangle AOB

∠OAB+∠OBA+∠AOB =180° (angle sum property)

by eq.no (1)

90°+∠AOB=180°

therefore,

∠AOB=90°

Hence proved.