๐ Topic Summary
In geometry, proving lines are parallel involves demonstrating that certain angle relationships exist when a transversal intersects the lines. If corresponding angles are congruent, alternate interior angles are congruent, or alternate exterior angles are congruent, then the lines are parallel. Also, if same-side interior angles or same-side exterior angles are supplementary (add up to 180 degrees), the lines are parallel. These angle relationships are based on postulates and theorems that allow us to deduce parallelism.
๐ Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Transversal |
A. Angles that lie on the same side of the transversal and between the two lines. |
| 2. Corresponding Angles |
B. A line that intersects two or more other lines. |
| 3. Alternate Interior Angles |
C. Angles that lie on opposite sides of the transversal and between the two lines. |
| 4. Same-Side Interior Angles |
D. Angles that lie on the same side of the transversal and outside the two lines. |
| 5. Alternate Exterior Angles |
E. Angles that occupy the same relative position at each intersection where a transversal crosses two lines. |
โ๏ธ Part B: Fill in the Blanks
When a transversal intersects two lines, if ____________________ angles are congruent, then the lines are parallel. If same-side interior angles are ____________________, then the lines are also parallel. The converse of the ____________________ angle theorem can be used to prove lines parallel.
๐ค Part C: Critical Thinking
Explain how the concept of slope relates to proving that two lines are parallel on a coordinate plane. Why does having the same slope guarantee parallelism?