## Theorem 3-1 Alternate Interior Angles Theorem

### If a transversal intersects two parallel lines, then alternate interior angles are congruent

The Alternate Interior Angles Theorem is a fundamental theorem in geometry. It states that if two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.

More specifically, if two parallel lines are intersected by a third line, which is known as the transversal, then the alternate interior angles on either side of the transversal are congruent. In other words, if we draw two parallel lines, and then draw a line that intersects these parallel lines at some angle, then the angles that are closest together but on opposite sides of the transversal line are congruent.

To use this theorem, it is important to be clear on the following terms:

– Parallel lines: Lines that never intersect and are always the same distance apart.

– Transversal: A line that intersects two or more other lines at different points.

Once these terms are clear, it becomes evident that the alternate interior angles theorem holds true. The theorem is then used to find unknown angles in a given diagram by identifying which angles are alternate interior angles and then using their congruence to solve for the unknown angle.

##### More Answers:

Mastering Geometry: The Same-Side Exterior Angles Theorem For Finding Missing Angles And Proving TheoremsMaster The Alternate Exterior Angles Theorem And Solve Problems With Parallel Lines And Transversals

Mastering Geometry: The Same-Side Interior Angles Theorem.