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.
First, we need to define parallel and perpendicular lines.
Watch this video to learn how to identify these types of lines.
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.
Read this article and watch the video. These materials use language we will explore in later sections, but you should understand how to calculate the angle of a transversal. Pay close attention to how to calculate an unknown angle on a transversal line.
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.
Read this article and watch the videos. The corresponding angle postulate states that corresponding angles have approximately the same degree measurement. Watch the videos to see examples of how to calculate corresponding angles and their measurements. Carefully read examples 1–3.
Then, complete review questions 2, 3, 4, 11, 12, 13, 14, and 15 and check your answers.
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.
Read this article and watch the videos. Pay attention to the alternate interior angles theorem, which states that alternate interior angles are congruent. Do not focus on the proof, but pay attention to the example on measuring angles.
Then, complete review questions 1, 2, 6, 7, and 8 and check your answers.
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.
Read this article and watch the videos. Pay attention to the alternate exterior angles theorem. As in the last section, do not focus on the proofs. Rather, focus on the examples that demonstrate how to recognize alternate exterior angles, measure angles, and apply these concepts to the real world.
Then, complete review questions 1, 2, 3, 4, 13, 14, and 15 and check your answers.
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.
Read this article and watch the videos. Pay attention to the same side interior angle theorem. Read the examples on recognizing same side interior angles and measuring angles closely.
Then, complete review questions 1–5 and check your answers.
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.
Watch this video on how to use the distance formula to find the distance between two points and a few examples of how to do it.
After you watch the video, complete this assessment and check your answers.