## What happens if two parallel lines are cut by two Transversals?

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

### Can there be two Transversals?

When a parallel-lines-with-transversal drawing contains more than three lines, identifying congruent and supplementary angles can be kind of challenging. The following figure shows you two parallel lines with two transversals.

**Are parallel lines cut by transversal supplementary?**

When the lines are parallel, the interior angles on the same side of the transversal are supplementary. If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

**What theorem proves lines are parallel?**

If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

## Do transversal lines have to be parallel?

First, if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel. Second, if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

### How do you prove two lines are supplementary?

Theorem 10.4: If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles. Theorem 10.5: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles.

**How do you justify if two lines are parallel?**

The first is if the corresponding angles, the angles that are on the same corner at each intersection, are equal, then the lines are parallel. The second is if the alternate interior angles, the angles that are on opposite sides of the transversal and inside the parallel lines, are equal, then the lines are parallel.