CBSE Class 9 Maths Parallel Lines and Transversals

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plz answer urgently dear experts lines and angles question :

If two lines are parallel then prove that any pair of bisictors of thier alternate interior angle is also parallel.

Q 19

kindly give solution to the question in the image.

the diagram for the 8th question.

FIND X AN D Y
 If a transversal intersects two parallel lines, then prove that each pair of consecutive interior angles are supplementary.
 Show that in the given figure, AB  EF.
 If two lines are intersected by a transversal in such a way that the bisector of a pair of angles are parallel, show that the two lines are parallel.