Question

12. In the figure ABCD is a parallelogram and AO and BO are bisectors of ZA and ZB respectively
(1) equal
What is the measure of ZAOB?
D
С
A
B
hinnat noh other and are equal then is it a​

Answer 1

Answer:

✪ Given : In ||gm ABCD, AO and BO are angle bisectors of ∠A and ∠B respectively.

✪ To prove : ∠AOB = 90°

✪ Proof : Since in ||gm, opposite sides are parallel so here too AD || BC.

∠A + ∠B = 180° [Sum of interior consecutive ∠s]

Dividing above equation by 2

½ ∠A + ½ ∠B = ½ × 180°

➣ Now, ½ ∠A = ∠OAB and ½ ∠B = ∠OBA

Therefore,

∠OAB + ∠OBA = 90°

➣ In ∆AOB, due to angle sum property.

∠OAB + ∠OBA + ∠AOB = 180°

90° + ∠AOB = 180°

∠AOB = 90°

✪ Q.E.D

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Answer 2

Answer:

hope so it will helpful to you