Question

if two lines are intersected in such a way that the bisector of a pair of corresponding angles are parallel show that the given lines are parallel to each other.



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Answer 1

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Answer 2

]Answer

The transversal AD intersects the two lines PQ and RS at points B and C respectively. BE is the bisector of ∠ABQ and CF is the bisector of ∠BCS.

As, BE is the bisector of ∠ABQ, then,

∠ABE=21∠ABQ

In the same way,

∠BCF=21∠BCS

Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,

∠ABE=∠BCF

21∠ABQ=21∠BCS

∠ABQ=∠BCS

Therefore, by the converse of corresponding angle axiom,

PQ∥RS.