Constructing Parallel Lines
Lesson 5 of 13
Objective: SWBAT construct parallel lines using a compass and a straightedge and describe the relationship between the angles formed by the construction.
As students walk in the room, I hand them a compass, protractor and ruler (straightedge). There are several different types of compasses and I have students choose which one they prefer to use (MP5). I instruct the students to draw two angles, one acute and one obtuse. The students then construct a copy of each of the angles. This will help the students prepare for constructing parallel lines.
We start the mini-lesson by reviewing the term "parallel lines." I use the definition, "Parallel lines are lines in the same plane that never intersect." It is important to discuss that parallel lines are equidistant from eachother throughout the entire length of the lines (MP6).
Students then learn how to construct a parallel line through a point not on the line using the angle-copy method. I first show a demonstration from Math Open Reference. After the demonstration, students practice the construction. Students should recognize the similarities between this construction and the construction from the Do Now.
After students have constructed the parallel lines, we discuss why it works. We discuss the term "corresponding angles" and the theorem that says "if corresponding angles formed by two lines intersected by a transversal are congruent, then the two lines are parallel" (G.CO.9). Students can measure all of the angles formed to verify the theorem. I also point out the alternate interior angles and the relationship between them.
*Depending on the level of my class, I sometimes talk about Euclid's Parallel Postulate and how it has been used as a basis for Geometry classes.
In this section, students practice constructing parallel lines. They also answer questions involving the relationship between the angles formed when two parallel lines are cut by a transversal. See the, "Constructing Parallel Lines Practice video" for a further explanation.
After about 15 minutes, I go over the worksheet with the students.
Group Discussion: How many lines can pass through a point not on a line and be parallel to that line?
Compare students constructions from question 1 on the worksheet "Parallel Lines Practice." Hand out a piece of patty paper or tracing paper. Instruct students to trace over the parallel lines from question 1. Then students then swap worksheets and place their patty paper on top of their partner's parallel lines. They can swap again to see if they get the same results. Although the measure of the angles formed may be different, the parallel lines will be the same distance apart.
This activity demonstrates Playfair's Axiom, "In a plane, exactly one line can be drawn through any point not on a given line parallel to the given line."
Homework: Students for homework practice finding the measures of angles formed when two parallel lines are intersected by a transversal.