what type of angle is formed
at the
the point of intersection of
the angle bisector of
two
adjacent angles of a
angles of a parallelogram?
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In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.
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asked Dec 22, 2017 in Class IX Maths by saurav24 Expert (1.4k points)
In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.
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2 Answers
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answered Dec 23, 2017 by ashu Premium (930 points)

Given : A parallelogram ABCD such that the bisectors of adjacent angles A and B intersect at P.
To prove : ∠APB = 90°
Proof : Since ABCD is a | | gm
∴ AD | | BC
⇒ ∠A + ∠B = 180° [sum of consecutive interior angle]
⇒ 1 / 2 ∠A + 1 / 2 ∠B = 90°
⇒ ∠1 + ∠2 = 90° ---- (i)
[∵ AP is the bisector of ∠A and BP is the bisector of ∠B ]
∴ ∠1 = 1 / 2 ∠A and ∠2 = 1 / 2 ∠B]
Now, △APB , we have
∠1 + ∠APB + ∠2 = 180° [sum of three angles of a △]
⇒ 90° + ∠APB + ∠2 = 180° [ ∵ ∠1 + ∠2 = 90° from (i)]
Hence, ∠APB = 90°
Step-by-step explanation:
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