Question

If a transversal intersects two lines such that a pair of corresponding angle is equal, then the two
lines are parallel to each other, Prove it.​

Answer 1

Given:

• If a transversal intersects two lines such that a pair of corresponding angle is equal.

To Prove:

• the twolines are parallel to each other.

Solution:

now in the figure, transversal AD intersects two lines PQ and RS at the points B and C

so, we have to prove PQ || RS

now in the fig,

as AD is the transversal line so,

$: ⟹ \sf \angle \: abq = \angle bcs \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt as \: corresponding \: anlges \: are \: equal$

and these are the corresponding angles from by the transversal AD and Pq and Rs

so,when a travelsal makes corresponding angles which are equal then,the lines are parallel to each other

hence proved PQ || RS

hope this helps.!!