Question

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

Answer 1

Given:

• ABCD is a parallelogram
• ∠A and ∠B meet at point O

To prove:

• That ∠AOB is a right angle.

Solution:

Let us take ∠A=2x and ∠B=2y

Since, it is given that ABCD is a parallelogram and adjacent angles are supplementary ,we have

⇛2x+2y=180°

⇛2(x+y)=180°

⇛x+y=90°

In ∆AOB ,we have

∠OAB=x(OA bisects ∠A) (given)

∠OBA=y(OB bisects ∠B) (given)

Thus, using angle sum property in ∆AOB,we will have

⇛x + y +∠AOB = 180°

⇛90° + ∠AOB = 180°

⇛∠AOB = 180° - 90°

⇛∠AOB = 90°

Hence,proved that ∠AOB is a right angle as Right angle=90°.

Answer 2

Given:

• ABCD is a parallelogram
• ∠A and ∠B meet at point O

To prove:

• That ∠AOB is a right angle.

Solution:

Let us take ∠A=2x and ∠B=2y

Since, it is given that ABCD is a parallelogram and adjacent angles are supplementary ,we have

⇛2x+2y=180°

⇛2(x+y)=180°

⇛x+y=90°

In ∆AOB ,we have

∠OAB=x(OA bisects ∠A) (given)

∠OBA=y(OB bisects ∠B) (given)

Thus, using angle sum property in ∆AOB,we will have

⇛x + y +∠AOB = 180°

⇛90° + ∠AOB = 180°

⇛∠AOB = 180° - 90°

⇛∠AOB = 90°

Hence,proved that ∠AOB is a right angle as Right angle=90°.