Q. 26

If two lines are intersected by a transversal in such a way that the bisectors of a pair of corresponding angles are parallel, show that two lines are parallel.

Answer :

Given: Two lines AB and CD are intersected by the transversal EF and GP is the angle bisector of ∠EGB and HQ is the bisector of ∠GHD. Also GP || HQ 
To Prove: AB || CD
Proof: Since GP || HQ and EF is the transversal
    Þ ∠1 = ∠3
Þ 2 ∠1 = 2 ∠3    
    
... ∠EGB = ∠GHD
But these are corresponding angles of AB and CD with the transversal EF. 
... AB || CD

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