Question

State the condition when a transversal intersects two parallel lines .​

Answer 1

Answer:

First, if a transversal intersects two parallel lines, then the alternate interior angles are congruent. ... The proposition continues by stating that on a transversal of two parallel lines, corresponding angles are congruent and the interior angles on the same side are equal to two right angles.

Answer 2

Step-by-step explanation:

Let AB and CD are the two parallel Lines cut by a transversal line XY.

• The transversal line XY create 4 angles $(\angle 1,~ \angle 2,~ \angle 3,~ \angle 4)$ at the intersection with line AB and 4 angles $(\angle 5,~ \angle 6, ~\angle 7, ~\angle 8)$ at the intersection with line CD.
• The angles that lie inside the two parallel lines are called interior angles and the measures of alternate interior angles are equal$(\angle 4= \angle 6 ~\& ~ \angle 3= \angle 5)$.  
• The angles that lie outside the two parallel lines are called exterior angles and the measures of alternate interior angles are equal $(\angle 1= \angle 7 ~\& ~ \angle 2= \angle 8)$ .
• The measures of same side interior angles $(\angle 3+\angle4= \angle 5+ \angle 6=180^{o} )$ and exterior angles $(\angle 1+\angle2= \angle 7+ \angle 8=180^{o} )$ add to 180°.  
• When two parallel lines are cut by a transversal, four pairs of corresponding angles are formed and they are congruent.  $(\angle 1= \angle 5,~ \angle 2= \angle 6, ~\angle 3= \angle 7 ~\& ~ \angle 4= \angle 8)$