Geometry / Unit 3: Parallel and Perpendicular Lines
3.3 Parallel Lines and Angle Measures
Notes
When a transversal crosses parallel lines, the angle pairs have fixed relationships.
- Corresponding angles are congruent.
- Alternate interior angles are congruent. Alternate exterior angles are congruent.
- Same-side interior angles are supplementary (add to $180^\circ$).
- Example: lines are parallel, and one angle is $70^\circ$. Its alternate interior angle is $70^\circ$ and its same-side interior angle is $110^\circ$.
Practice
Parallel lines are cut by a transversal. Two corresponding angles measure $(3x + 10)^\circ$ and $(5x - 30)^\circ$. Find $x$.
Corresponding angles are congruent: $3x + 10 = 5x - 30$, so $2x = 40$.
Parallel lines are cut by a transversal. One same-side interior angle is $58^\circ$. What is the other?
Same-side interior angles are supplementary: $180 - 58 = 122$.
Parallel lines are cut by a transversal. Alternate exterior angles measure $(2x + 15)^\circ$ and $(x + 40)^\circ$. What is the angle measure?
$2x + 15 = x + 40$ gives $x = 25$, so the angle is $65^\circ$.
Ready for more? Take the Unit 3 test.