Corresponding Angles: Definition, Theorem & Examples

Corresponding Angles: Definition, Theorem & Examples
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  • 0:00 Definitions
  • 2:10 Corresponding Angles Theorem
  • 2:50 Examples
  • 4:20 Lesson Summary
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Lesson Transcript
Instructor: Sarah Spitzig

Sarah has taught secondary math and English in three states, and is currently living and working in Ontario, Canada. She has recently earned a Master's degree.

In this lesson, you will learn how to identify corresponding angles. You will also learn how to use a theorem to find missing angles and solve everyday geometry problems.

Definitions

Before getting into the definition of corresponding angles, let's first go over a few basics about angles, transversal lines, and parallel lines.

An angle is formed when two rays, a line with one endpoint, meet at one point. This one point where two rays meet is called a vertex. The angle is formed by the distance between the two rays. Angles in geometry are often referred to using the < symbol, so angle A would be written as <A.

angle

A transversal line is a line that crosses or passes through two other lines. Sometimes the two other lines are parallel, and the transversal passes through both lines at the same angle. However, the two other lines do not have to be parallel in order for a transversal to cross them, as you can see here:

transversal

A straight angle, also called a flat angle, is formed by a straight line. The measure of this angle is 180 degrees. A straight angle can also be formed by two or more angles that sum to 180 degrees.

In the image on the right, <1 + <2 = 180.

straight angle

Parallel lines are two lines on a two-dimensional plane that never meet or cross. When a transversal passes through parallel lines, there are special properties about the angles that are formed that do not occur when the lines are not parallel. Notice the arrows on lines m and n towards the left. These arrows indicate that lines m and n are parallel.

parallel lines

Corresponding angles are formed when a transversal passes through two lines. The angles that are formed in the same position, in terms of the transversal, are corresponding angles.

corresponding angles

In this picture of a window pane, <a and <b are corresponding angles because they are in the same position. They are both above the parallel lines and to the right of the transversal.

real life CA

Corresponding Angles Theorem

The Corresponding Angles Theorem states:

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

A theorem is a proven statement or an accepted idea that has been shown to be true. The converse of this theorem, which is basically the opposite, is also a proven statement:

If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

These theorems can be used to solve problems in geometry and to find missing information. The diagram shows which pairs of angles are equal and corresponding. Notice that the lines are parallel.

corresponding angles

Examples

Find the measure of the missing angles in the following diagram. Assume the lines are parallel.

CA example

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