# Vertical Angles in Geometry: Definition & Examples

Coming up next: What Are Adjacent Angles? - Definition & Examples

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 1:09 More Examples
• 1:28 Congruency Property
• 1:42 Proof
• 3:09 Finding Angle Measures
• 3:47 What Vertical Angles are Not
• 4:09 Lesson Summary
Save Save

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: David Liano
After completing this lesson, you will be able to identify and draw vertical angles. You will also be able to state the properties of vertical angles. After the lesson, test yourself with a quiz.

## Definition: Vertical Angles

Vertical angles are a pair of non-adjacent angles formed when two lines intersect. We see intersecting lines all the time in our real world. Here, we see two vapor trails that intersect. Therefore, they have created the pair of vertical angles labeled as 1 and 2.

Here is a pair of vertical angles formed in nature and that are more terrestrial.

If we draw a pair of intersecting lines, we have created two pairs of vertical angles. Here, angles AOC and BOD are a pair of vertical angles. Angles AOB and COD are also a pair of vertical angles.

Notice that vertical angles are never adjacent angles. In other words, they never share a side. For example, angles AOC and AOB are not a pair vertical angles, but they are adjacent angles. However, vertical angles always have a common vertex. Here, each pair of vertical angles share vertex O.

## Vertical Angles: More Examples

Let's look at some more examples of vertical angles.

Line c intersects two lines, a and b. Vertical angles are formed at each intersection. The vertical pairs of angles are as follows:

1 and 6
2 and 5
3 and 8
4 and 7

## Vertical Angles: Congruency Property

A primary property of vertical angles is that they are congruent. In other words, they have the same angle measure. Here, if we add in the angle measures, we'll see that vertical angles are congruent.

## Proof

Let's do a simple proof for this. Before we begin, we should acknowledge some definitions and theorems in geometry. First of all, a linear pair of angles is a pair of adjacent angles. Their non-common sides are always opposite rays. In addition, angles that form a linear pair are also supplementary, so their sum is always 180 degrees. Here is our proof.

1. Lines m and n intersect forming angles 1, 2, 3, and 4 (given).
2. Angles 1 and 2 are a linear pair, so they are supplementary (definition of linear pair).
3. Angle 1 + angle 2 = 180 degrees (definition of supplementary angles).
4. Angles 2 and 3 are a linear pair, so they are supplementary (definition of linear pair).
5. Angle 2 + angle 3 = 180 degrees (definition of supplementary angles).
6. Angle 1 + angle 2 = angle 2 + angle 3 (substitution; see statements 3 and 5).
7. Angle 1 = angle 3 (subtract angle 2 from the equation in statement 6).
QED (our proof is complete)

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.