Question

when a transversal Þ intersects Parallel lines q and r,then angle a is always equal to angle b. true/false​

Answer 1

Answer:

False is the answer.......

Answer 2

If a transversal intersect two parallel line then alternate interior angles are equalis true.
We can prove it by using converse of the corresponding angles axiom which states .
"If a transversal intersects two lines such that a pair of corresponding angles is equal then the two lines are parallel to each other."
∠BQR=∠CRQ (alt. angles)
let us assume they are equal show AB||CD
∠BQR=∠PQA--------------------1 (vertically opposite angle)
∠BQR=∠QRC -------------------2 (assumed)
so from 1 and 2∠PQA=∠QRC
as they are corresponding angles
so, AB∣∣CD {converse of corresponding angle axiom}

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