Unit 2: Parallel and Perpendicular Lines
Parallel lines are lines in a plane that do not intersect. Perpendicular lines intersect at a right angle: 90 degrees. We see parallel and perpendicular lines all around us in chairs, tables, buildings, fences, and roadways.
In this unit, we will explore what happens when parallel lines cross other lines and how the angles they form relate to one another.
Completing this unit should take you approximately 4 hours.
2.1: Parallel, Perpendicular, and Skew Lines
First, we need to define parallel and perpendicular lines.
2.2: Angles and Transversals
In this section, we learn about transversal lines, which are lines that cut across two parallel lines. Transversal lines create angles as they cut across the parallel lines, and we can calculate these angels based on our knowledge of geometry thus far.
2.3: Corresponding Angles
Corresponding angles are transversal angles that are in the same location on two parallel lines. By observing the location of angles which a transversal on two parallel lines makes, we can show that corresponding angles must have the about same degree measurement.
2.4: Alternate Interior Angles
When a transversal line cuts across parallel lines, we can identify the different angles it creates. In the following three sections we explore each type of angle the transversal line makes.
First, we investigate alternate interior angles. These are the angles in between the two parallel lines, but on opposite sides of the transversal line. These angles are about equal to each other.
2.5: Alternate Exterior Angles
The next types of angles a transversal line produces are alternate exterior angles. Alternate exterior angles are on the exterior, or outside, of the parallel lines, and are on opposite sides of the transversal line. Alternate exterior angles are congruent.
2.6: Same Side Interior Angles
The last type of angle a transversal line produces are same side interior angles. These angles occur on the same side of the transversal line in between the two parallel lines. Same side interior angles are supplementary.
2.7: Distance Formula in the Coordinate Plane
Now that we understand how angles are formed between lines in the coordinate plane, we can use the distance formula to determine the distance between any two points in the coordinate plane.