## alternate interior angles

### Alternate interior angles are a pair of angles that are on opposite sides of a transversal and inside a pair of parallel lines

Alternate interior angles are a pair of angles that are on opposite sides of a transversal and inside a pair of parallel lines. They are formed when a transversal intersects two parallel lines, creating eight angles in total.

The alternate interior angles lie on the inside of the two parallel lines and are non-adjacent angles. In other words, they do not share a common vertex or a common side. Instead, they are separated by one of the transversal lines.

The key property of alternate interior angles is that they are equal in measure. This means that if two lines are parallel and a transversal intersects them, the alternate interior angles will have the same measurement. This property makes alternate interior angles useful in many geometric proofs and calculations.

To better understand alternate interior angles, let’s consider an example. Suppose we have two parallel lines, line A and line B, with a transversal line intersecting them. This will create four pairs of alternate interior angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8.

According to the property mentioned earlier, angle 1 and angle 5 will have the same measure, angle 2 and angle 6 will be equal, and so on. So, if angle 1 measures 60 degrees, then angle 5 will also measure 60 degrees. Similarly, if angle 2 measures 40 degrees, angle 6 will also measure 40 degrees.

The concept of alternate interior angles is not limited to parallel lines. It can also be applied to other types of angle relationships, such as when a transversal intersects a pair of congruent lines or a pair of lines that intersect at a point outside the lines.

In summary, alternate interior angles are a pair of angles that lie inside a pair of parallel lines, and they have the same measure. Understanding this concept can be helpful in solving geometry problems and proving geometric theorems.

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