Proving Lines Parallel
Overview
Lesson 18 used angle pairs to find measures when the lines were already known to be parallel. This lesson runs the logic in reverse: if one of the angle-pair conditions holds, then the lines are parallel. You will use the conditions two ways — to verify, from given measures, whether lines are parallel, and to force the lines to be parallel by solving for the value of x that makes a condition true.
Vocabulary
- Parallel Lines
- Lines that lie in the same plane and do not intersect.
- Transversal
- A line that intersects two or more other lines at different points, all in the same plane.
- Converse
- The statement formed by switching the hypothesis and the conclusion of a conditional statement. Each parallel-line condition in this lesson is the converse of a property from the previous lesson.
Main Ideas
- If alternate interior angles are congruent, then the two lines intersected by the transversal are parallel.
- If alternate exterior angles are congruent, then the two lines intersected by the transversal are parallel.
- If corresponding angles are congruent, then the two lines intersected by the transversal are parallel.
- If consecutive interior angles are supplementary, then the two lines intersected by the transversal are parallel.
- Vertical angles are congruent and a linear pair is supplementary at any single intersection, parallel or not — so neither one can ever be used to prove that lines are parallel.
- To verify: check whether the given measures satisfy one of the four conditions. To force: set up the equation the condition requires (expressions equal, or expressions summing to 180°) and solve for x.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Adjust the figure and decide, from the angle relationships, whether the lines are parallel.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.