Section 1
Definition of Parallel Lines
Property
Two lines are parallel if and only if they never intersect, no matter how far they are extended. Parallel lines are always the same distance apart and run in exactly the same direction.
In this Grade 4 lesson from The Art of Problem Solving: Prealgebra (AMC 8), students explore parallel lines and the angle relationships formed when a transversal crosses them. Learners discover that the eight angles created fall into two groups of four equal angles, where each angle in one group is supplementary to each angle in the other, and apply this to find unknown angle measures. The lesson also introduces the problem-solving technique of adding an auxiliary parallel line to diagrams in order to solve multi-step geometry problems.
Section 1
Definition of Parallel Lines
Two lines are parallel if and only if they never intersect, no matter how far they are extended. Parallel lines are always the same distance apart and run in exactly the same direction.
Section 2
Parallel Lines and Transversals
If two lines are parallel, and a third line (a transversal) cuts across both, then corresponding angles at the points of intersection have the same measure. The translation that moves the intersection point on the first line to the intersection point on the second line will also map the first line onto the second, showing the angles are congruent.
Conversely, if a transversal cuts across two lines such that the corresponding angles are equal, then the two lines are parallel.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
Definition of Parallel Lines
Two lines are parallel if and only if they never intersect, no matter how far they are extended. Parallel lines are always the same distance apart and run in exactly the same direction.
Section 2
Parallel Lines and Transversals
If two lines are parallel, and a third line (a transversal) cuts across both, then corresponding angles at the points of intersection have the same measure. The translation that moves the intersection point on the first line to the intersection point on the second line will also map the first line onto the second, showing the angles are congruent.
Conversely, if a transversal cuts across two lines such that the corresponding angles are equal, then the two lines are parallel.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter