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If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel

The transversal  intersects the two lines  and  at points  and  respectively.  is the bisector of  and  is the bisector of .

As,  is the bisector of , then,

In the same way,

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

Therefore, by the converse of corresponding angle axiom,

.




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