Question

if a transversal intersects two line such that a pair corresponding angles is equal then the two line are parallel to each other proof it ​

Answer 1

Answer:We know that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines ate parallel to each other. Hence, AB║ EF Proved.

Step-by-step explanation:

Answer 2

Answer:

We know that if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines ate parallel to each other. Hence, AB║ EF Proved

Theorem 5: If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

Solution:

lines & angles 12

Given: A transversal EF intersects two lines AB and CD at P and Q respectively.

To Prove: AB ||CD

Proof: ∠1 + ∠2 = 180° ………..equation (i) (Given)

∠1 + ∠3 = 180° …………..equation (ii) (Linear Pair)

From equations (i) and (ii)

∠1 + ∠2 = ∠1 + ∠3

Or, ∠1 + ∠2 - ∠1 = ∠3

Or, ∠2 = ∠3

But these are alternate interior angles. We know that if a transversal intersects two lines such that the pair of alternate interior angles are equal, then the lines are parallel.

Hence, AB║CD Proved.