Alternate Interior Angles Explained: Geometry Concepts & Examples

📚 Quick Study Guide

• 📐 Definition: Alternate interior angles are formed when a transversal intersects two lines. They lie on the inside of the two lines and on opposite sides of the transversal.
• 🤝 Parallel Lines: If the two lines intersected by the transversal are parallel, then the alternate interior angles are congruent (equal).
• 🔥 Converse: If alternate interior angles are congruent, then the two lines are parallel.
• ✏️ Theorem: Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
• 🧮 Formula: If line $l$ is parallel to line $m$, and transversal $t$ intersects both, then the measures of alternate interior angles are equal: $\angle 1 = \angle 2$.

Practice Quiz

1. What are alternate interior angles?
   1. Angles on the same side of the transversal.
   2. Angles on the outside of the two lines.
   3. Angles on the inside of the two lines and on opposite sides of the transversal.
   4. Angles that are adjacent.
2. If two parallel lines are cut by a transversal, what is the relationship between the alternate interior angles?
   1. They are supplementary.
   2. They are complementary.
   3. They are congruent.
   4. They are right angles.
3. If two lines are cut by a transversal and the alternate interior angles are congruent, what can be concluded?
   1. The lines are perpendicular.
   2. The lines are parallel.
   3. The lines intersect at a 45-degree angle.
   4. The lines are skew.
4. Angle A and Angle B are alternate interior angles formed by a transversal cutting two parallel lines. If Angle A measures 60 degrees, what is the measure of Angle B?
   1. 30 degrees
   2. 60 degrees
   3. 120 degrees
   4. 90 degrees
5. Which of the following pairs of angles are alternate interior angles?
   1. Corresponding angles
   2. Vertical angles
   3. Same-side interior angles
   4. Alternate exterior angles
6. In the given diagram, line 'p' and line 'q' are intersected by transversal 'r'. If ∠3 and ∠6 are alternate interior angles, which statement must be true for 'p' and 'q' to be parallel?
   1. ∠3 and ∠6 must be supplementary.
   2. ∠3 and ∠6 must be congruent.
   3. ∠3 and ∠6 must be complementary.
   4. ∠3 and ∠6 must be right angles.
7. What happens to the measure of the alternate interior angles when the two lines intersected by the transversal are NOT parallel?
   1. They are always congruent.
   2. They are always supplementary.
   3. They are not necessarily congruent.
   4. They become vertical angles.