Question

Class:- 9th
Que:- If two parallel lines are intersected by a transversal, prove that the bisector of two pairs of interior angles from a rectangle.​

Answer 1

Given: Two parallel lines AB and CD and a transversal EF intersect them at G and H respectively. GM, HM, GL and HL are the bisectors of the two pairs of interior angles.

To Prove: GMHL is a rectangle.

Proof:

∵AB∥CD

∴∠AGH=∠DHG (Alternate interior angles)

⇒

2

1

∠AGH=

2

1

∠DHG

⇒∠1=∠2

(GM & HL are bisectors of ∠AGH and ∠DHG respectively)

Hence, GMHL is a rectangle

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