Question

If a transversal intersects two lines such that bisector of corresponding angles are parallel.prove that 2 lines are parallel​

Answer 1

Observe the above figure;

Given: HI || JK, HI and JK are bisectors.

To prove : AB || CD

Proof: HI bisects angle EHB and JK bisects angle HJD.

Hence, angle EHI congruent to angle IHB and angle HJK congruent to angle KJD.

But angle EHI is congruent to angle HJK as HI || JK and these are corresponding angles.

Hence, angle EHB is also congruent to angle HJD as HI and JK are angle bisectors.

Hence by corresponding angle test,

Line AB || Line CD.

Hence proved.





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