Question

in a parallelogram show that the angle bisector of two adjacent angle intersect at a right angle

Answer 1

Solution:

Let the adjecent angle of ||gm be x & y.

Then, x + y = 180° [sum of adjecent angles are supplementary]

X/2 + y/2 = 90°.....(1)

Now, let angle bisector meet at O

Then, Angle o + x/2 + y/2 = 180°

O +90 = 180

O = 90° [proved]

_______________

Amrit

Answer 2

Answer:

we know that,

                       ABCD is a ||gm

Now, angle A + angle B =    $180^{0}$

         1/2 angle A + 1/2 angle B = $90^{0}$ --(1)

In Triangle AOB,

angle BAO + angle AOB + angle ABO = 180 --(Angle sum prop.)

1. We take 1/2 angle A instead of angle BAO
2. WE take 1/2 angle B instead of angle ABO

1/2 A + 1/2 B + angle AOB = 180 --(Angle sum prop.)

angle AOB = 180 - ( 1/2 A + 1/2 B ) -- from 1

angle AOB = 180 - 90

angle AOB = $90^{0}$

∴ Angle Bisecting of 2 adjacent angles intersect at $90^{0}$