Alternate Interior Angles – Definition – Examples – Properties

What are alternate interior angles?

The term alternate interior angles is often used when two lines are intersected by a third line(transversal).

Alternate interior angles are formed when two lines are intersected by a third line. The third line is known as the transversal line.

Alternate interior angles are formed when a transversal intersect two parallel or non-parallel lines.

Definition:

Alternate angles are the pair of non-adjacent angles with opposite side of the transversal line and on the inner or interior side of the two parallel or non-parallel lines. If two angles on the same side of the transversal line, are known as consecutive interior angles.

Why the angles are called alternate interior angles.

Angles are called alternate interior angles because they are located opposite, and on the interior of the two lines.

In figure above, both angle 1 and angle 2 are located on the inner side or in between the lines. They are also opposite side of the transversal and not adjacent to each other.

Hence angle 1 and angle 2 are a pair of alternate interior angles.

The other pair of alternate interior angles is angle 3 and angle 4.

If two parallel lines are intersected by transversal line, then the pairs of alternate angles are congruent. If the alternate angles are equal, then two lines are parallel.

Here transversal, intersecting lines m and n. Since alternate interior angles are congruent, both angles have same measure.

However, if a transversal intersects through two non-parallel lines, the pairs of alternate angles formed are not congruent and have no relationship in any way.

Note : We can easily spot a pair of alternate interior angles because they form a Z-shape or backward Z-shape.

To understand more clearly what alternate interior angles are, see the following properties.

Properties of Alternate Angles

• Alternate interior angles are formed when a transversal intersect two parallel or non-parallel lines.

• Alternate interior angles that opposite each other are same in measure(congruent).

• The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is equal to 180.

• Alternate interior angles have no any specific properties, in case of non-parallel lines and are not congruent.