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Basic Geometry

Basic Geometry

At a Glance - Parallel Lines & Transversals

A transversal is a line that intersects two or more other lines. When it intersects parallel lines, many angles are congruent. Let's take a peek at what this means. Lines k and j are parallel. Line l is a transversal.

Parallel Lines

As we mentioned before, when this happens we get a bunch of pairs of congruent angles. These pairs have nifty vocabulary terms to go with them. Here they are:

  • Corresponding angles - angles that are in the same position on each line. There are four sets of these angles: Angles 1 & 5; 2 & 6; 3 & 7; 4 & 8.
  • Alternate interior angles - angles on the opposite sides of the transversal and on the interior of the parallel lines. There are two sets of alternate interior angles: Angles 4 & 6 and Angles 3 & 5.
  • Alternate exterior angles - angles on opposite sides of the transversal and on the exterior of the parallel lines. There are two sets of alternate exterior angles: Angles 8 & 2 and Angles 1 & 7.

Look Out: these pairs of angles are congruent only when the transversal cuts parallel lines.

Example 1

Lines j and k are parallel.

Angle A = 120 degrees.

Plane jkl

Refer to this diagram for Exercises 1-4

Lines m, n, and o are parallel.

Plane mnop

Exercise 1

What angles are corresponding to Angle K?

Exercise 2

What is the measure of Angle K?

Exercise 3

Which angles have measurements of 75°?

Exercise 4

Which angles have measures of 105°?

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