Question

Ques- In the adjoining figure, ABCD is a parallelogram.
If angle bisectors of (angle)-A and (angle-)B meet at P. Prove that
angle-APB = 90°.
​

Answer 1

Answer:

Step-by-step explanation:

Since ABCD is a Parallelogram. Therefore,

AD || BC

AB is a transversal . Therefore ,

A + B = 180°. [ Consecutive interior angles]

Multiply both sides by 1/2 ,

1/2 A + 1/2 B = 1/2 (180°)

1/2 A + 1/2 B = 90° __【1】

Since, AP and PB are angle bisectors of A and B . Therefore,

Angle 1 = 1/2 A

Angle 2 = 1/2 B

Substitute the values in【1】,

Angle 1 + Angle 2 = 90°____【2】

Now, in ∆ APB,

1 + APB + 2 = 180°

90° + APB = 180°. [From 【2】]

APB = 90°

- HENCE PROVED

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