7. If a transversal intersects two lines parallel lines then prove that the bisectors of a pair of co
interior angles intersect each other at 90°.
Answers
Given : a transversal intersects two lines parallel lines
To find : bisectors of a pair of co interior angles intersect each other at 90°
Solution:
Let say L & M are two parallel lines
& a transversal line p intersect these lines
at A & B
∠A + ∠ B = 180 °
Angle bisector of A & B meet at P
∠ABP = ∠B/2
∠BAP = ∠A/2
in ΔAPB
∠ABP + ∠BAP + ∠APB = 180°
=> ∠B/2 + ∠A/2 + ∠APB = 180°
=> (∠B + ∠A)/2 + ∠APB = 180°
=> (180 °)/2 + ∠APB = 180°
=> 90° + ∠APB = 180°
=> ∠APB = 90°
QED
Hence Proved
bisectors of a pair of co interior angles intersect each other at 90°.
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