Why are alternate interior angles equal?

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal. The alternate interior angles can prove whether the given lines are parallel or not.

When two parallel lines are crossed by a transversal alternate interior angles are congruent?

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.

Are alternate interior angles are equal?

Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure.

Can transversal lines 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.

When two lines are parallel alternate angles are?

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 .

What are the angles formed by a transversal?

When two parallel lines are intersected by the transversal, eight angles are formed. The eight angles include corresponding angles, alternate interior and exterior angles, vertically opposite angles, and co-interior angles.

Which of the following angle pairs formed by a transversal that intersects two parallel lines are not congruent?

Alternate exterior angles two angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent.

What is interior angles on the same side of the transversal?

When a transversal intersects two lines, the two lines are parallel if and only if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary (sum to 180°).

Which theorem states that if two parallel lines cut by a transversal interior angles on the same side are supplementary?

alternate interior 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….Geometry.

What are the angles formed by a transversal and parallel lines?

If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .

When parallel lines are cut by a transversal same side interior angles are?

Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.

What is interior alternate angle?

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.