Parallel Lines and Transversals

When two parallel lines are intersected by a third line, called a transversal, eight different angles are formed at the intersections of the two lines.

These eight angles each have their own special names. Due to these angles being used so much in the real-world, their names will need to be memorized by you.

Before we get to naming the angles, let's first examine how the angles are formed. It will make memorizing their names easier.

  1. Alternate-Interior Angle
  2. Alternate-Exterior Angles
  3. Same-Side Interior Angles
  4. Same-side Exterior Angles
  5. Corresponding Angles

The names of the angles are related to their position to the transversal, and their second name is related to their position related to the two parallel lines and ignoring the transversal line as if it weren't there.

1. The word "Alternate" means 2 angles on opposite sides of the transversal.

2. The word "Same-side" means 2 angles on the same-side of the transversal.

3. "Corresponding" Angles are 2 angles that share the same-position in the two intersections of the lines.

In the first image, above and below the line are "alternates". As is left of the line and right of the line.

first

In the image below, when two lines are parallel, there are two sections: inbetween the parallel lines which is called the "Interior". Outside of the parallel lines is called the "Exterior" of the two lines. second


In order to name any angles formed by a transversal, you create their first name related to the transversal: same-side or alternate.

The second-half of the angles' names comes from their location between the two parallel lines: interior or exterior.

8 angles When being asked to name angles that are formed when two parallel lines are intersected by a transversal, first look at the two angles. Are they on the same-side of the transversal? If so, the first half of their name is same-side.

The second half of the name comes from the two angles' relationship to the two parallel lines (in this step you must ignore the transversal line). Are the two angles on the interior of the two parallel lines, or are they on the exterior of the two parallel lines? Give them their second name using either Interior or Exterior.

That's all their is to it!

Notice there was a fifth name called corresponding. This is a name used to describe angles that share the exact same position in each individual intersection of the two lines. Angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 are called Corresponding Angles. These pairs of angles share the same degrees and are therefore congruent to eachother.

Corr. Angles

So what does it look like when two parallel lines are intersected by a transversal and what degrees are each of the eight angles that are formed?

5 6 7

Notice all the patterns that are formed as you compare and contrast the different examples. The relationships you see will be true always when two parallel lines are intersected by a transversal.