##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Constructing Parallel Lines - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Constructing parallel lines with a compass and straightedge uses the converse of the parallel lines theorem. Creating congruent corresponding angles (or congruent AIA or AEA) guarantees parallel lines. The first step in **constructing parallel lines** is to draw a transversal through the given point to intersect the given line. Last, duplicate an angle created by the transversal and the given line.

When you're asked to construct a line through a point parallel to a given line, you are going to use three different methods. You could either choose corresponding angles, alternate interior angles or alternate exterior angles. So you are going to duplicate one of these three pairs of angles. But why does that work? Well, to do that let's take a little sketch.

If I had two lines and if I intersect these two lines by a transversal and I tell you that one pair of corresponding angles are congruent. Then the converse of the parallel lines theorem says that these two lines must be parallel. So this will also work if you have alternate exterior angles. So if you have angles that are on opposite sides of the transversal, or if you have alternate interior angles that are congruent. So you've three different ways of constructing parallel lines through a point.

Please enter your name.

Are you sure you want to delete this comment?

###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

so my teacher can't explain this in 5 weeks but I learn this in less than 3 minutes”

its hard to focus when the teacher is really really really goodlooking”

i like how it took you 3 minutes and 8 seconds to accomplish what my teacher couldn't in 3 days”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

##### Concept (1)

##### Sample Problems (3)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete