Question

Prove that the bisector of any two consecutive angles of parallelogram intersect at right angle

Answer 1

Answer:

2)Prove that the bisectors of any two consecutive angles of parallelogra,m intersect at right

angles

Answer 2

Given,

A parallelogram

To prove,

that the bisector of any two consecutive angles of parallelogram intersect at right angle

Solution,

ABCD is a parallelogram, which has the center O. Angle bisectors are OA and OB of angle A and angle B respectively.

Therefore, AD is parallel to BC and AB is the transversal.

Because the sum of consecutive interior angles is 180 degree

Angle A + Angle B  = 180

1/2 (Angle A) + 1/2 (Angle B) = 180/2

A/2 + B/2 = 90

Let A be angle x and B be angle y

So x + y = 90

In triangle AOB,

x + angle AOB + y = 180

x + y + angle AOB = 180

90 + angle AOB = 180

angle AOB = 180 - 90

angle AOB = 90

Therefore, the bisector of two consecutive angles of a parallelogram intersect at a right angle.