Question

in a parallelogram show that the angle bisectors of two adjacent angles intersect at right angle​

Answer 1

Answer:

hey

mate

Step-by-step explanation:

Given :-

ABCD is a parallelogram such that angles bisectors of adjacent angles A and angle B intersect at point P.

To be proof :-

∠APB = 90°

PROOF :

∠BAD + ∠ABC = 180°

[ ∴ AD║BC and ∠BAD and ∠ABC are consecutive interior angles ]

 

 

 

Now,

 

[ ∴ Sum of interior angles of triangle ]

 

⇒ 90° + ∠APB = 180°

⇒ ∠APB = 180° - 90°

∴ ∠APB = 90°

Hence

Proved.

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Answer 2

Step-by-step explanation:

In the Above figure

We have to prove that EFGH is a rectangle or adjacent angles intersect at right angle.

Proof

In llgm ABCD

Angle A+ Angle D=180°

1/2(A+D ),= 90..............................1/2×180=90°.......equation 1

In triangle AGD

Angle A+D+G=180°

90+G=180°

G=90°

Similarly prove all by Same steps

At last

<E=<F=<G=<H

(< means angle)

HENCE PROVED.

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