Question

if ABCD is a parallelogram and the angular bisectors of angle A and angle B meet at O , prove that angle AOB is a right angle

Answer 1

Answer:

Step-by-step explanation:

Refer to attachment for diagram.

We know that adjacent angles of a parallelogram are equal.

Hence, ∠ A + ∠ B = 180°

According to the diagram,

∠A = 2x ; ∠B = 2y

Hence 2x + 2y = 180°

⇒ x + y = 90°

Now consider the Δ AOB, Angle Sum Property states that sum of all angles  is 180°

⇒ x +∠O + y = 180°

⇒ ∠ O + 90° = 180°

⇒ ∠ O = 180 - 90 = 90°

Hence ∠AOB is a right angle.

Hence Proved !!

Hope it helped !!

Answer 2

$\bold{\huge{Hay!!}}$

$\bold{Dear\:user!!}$

$\bold{\underline{Question-}}$

if ABCD is a parallelogram and the angular bisectors of angle A and angle B meet at O , prove that angle AOB is a right angle

$\bold{\underline{Answer-}}$According to the question we know that In a parallelogram sum of adjacent angel is 180°

So,

ㄥA + ㄥD = 180°

Then,

In Δ AOD

A + ㄥD + ㄥO = 180°

$\frac{ \angle \: A}{2} + \frac{ \angle \: D}{2} + \angle \: O \: = 180$

90 + ㄥO = 180°

ㄥO = 90°

so, ㄥAOB is a right angle