# 9.3: Identification of Angles by Vertex and Ray

**At Grade**Created by: CK-12

**Practice**Identification of Angles by Vertex and Ray

Remember the skateboard park? Well, Cassie and James are talking about angles now. Take a look.

"Look at the angles of the walkway," James pointed out to Cassie as they looked at the design.

"What do you mean?"

"Well, there are many different angles that are all formed by the walkways. Each walkway has a line, then a turn. You see where the two lines meet, that is a vertex," James said.

"A what?"

"Boy, you need to pay attention in math class, then you would know the parts of an angle," James instructed.

Do you know the parts of an angle?

**Pay attention and you will know them by the end of the Concept.**

### Guidance

An *angle***is one of the key geometric figures that you will be working with in geometry. An angle is created when two rays connect at a common point.**

You can see here that the two rays are connected at a common endpoint, called a vertex. This forms the angle. An angle is named by points on the rays.

**This is angle** \begin{align*}ABC\end{align*}**The vertex** \begin{align*}B\end{align*}**is always in the middle. The symbol for angle looks like a small angle. Here is how we can name the angle.**

\begin{align*}\angle{ABC}\end{align*}

**Angle** \begin{align*}ABC\end{align*}**is named with this symbol.**

Name these two angles on your own. Be sure that the vertex is in the middle.

#### Example A

**Solution: \begin{align*}\angle{DEF}\end{align*} ∠DEF**

#### Example B

**Solution: \begin{align*}\angle{LMN}\end{align*} ∠LMN**

#### Example C

What is the point called where two rays meet in an angle?

**Solution: Vertex**

Now back to the angles with James and Cassie. Here is the original problem once again.

"Look at the angles of the walkway," James pointed out to Cassie as they looked at the design.

"What do you mean?"

"Well, there are many different angles that are all formed by the walkways. Each walkway has a line, then a turn. You see where the two lines meet, that is a vertex," James said.

"A what?"

"Boy, you need to pay attention in math class, then you would know the parts of an angle," James instructed.

Do you know the parts of an angle?

By now, you should know the parts of an angle. Here is the answer.

**An angle is formed when two rays meet at a common endpoint. This common endpoint is called the vertex.**

Now James and Cassie can continue to look at the diagram of the school.

### Vocabulary

Here are the vocabulary words in this Concept.

- Point
- a location in space that does not have size or shape.

- Ray
- a line that has one endpoint and continues indefinitely in one direction.

- Line
- a set of connected points without endpoints.

- Line Segment
- a set of connected points with two endpoints.

- Point of Intersection
- the point where two intersecting lines meet.

- Intersecting Lines
- lines that cross or meet at some point

- Parallel Lines
- Lines that do not cross or meet EVER and are equidistant.

- Angle
- a geometric figure formed by two rays that connect at a single point or vertex.

- Vertex
- The point of intersection of the lines or rays that form an angle

### Guided Practice

Here is one for you to try on your own.

Name the vertex and two rays of the following angle.

**Answer**

First, we can name the vertex of the angle. It is the point where the two rays meet.

The vertex is point E.

The two rays each start at the vertex and branch out.

The first one is ray ED. The second one is ray EF.

**These are our answers.**

### Video Review

Here is a video for review.

Khan Academy: Introduction to Angles

### Practice

Directions: Draw a picture to illustrate each of the named geometric figures.

1. \begin{align*}\overrightarrow{AB}\end{align*}

2. \begin{align*}\overleftrightarrow{CD}\end{align*}

3. \begin{align*}\overleftrightarrow{DE}\end{align*}

4. \begin{align*}\angle{ABC}\end{align*}

5. \begin{align*}\angle{LMN}\end{align*}

6. \begin{align*}\overline{XY}\end{align*}

7. \begin{align*}\overrightarrow{PQ}\end{align*}

8. \begin{align*}\overleftrightarrow{GH}\end{align*}

9. \begin{align*}\overleftrightarrow{AB} \parallel \overleftrightarrow{DE}\end{align*}

10. \begin{align*}\overleftrightarrow{LM} \parallel \overleftrightarrow{DE}\end{align*}

11. \begin{align*}\overleftrightarrow{RS} \parallel \overleftrightarrow{TU}\end{align*}

12. \begin{align*}\overline{DF} \parallel \overline{XY}\end{align*}

Directions: Define the following terms.

13. Ray

14. Line

15. Vertex

16. Line Segment

Angle

A geometric figure formed by two rays that connect at a single point or vertex.Intersecting lines

Intersecting lines are lines that cross or meet at some point.line

A line is a straight one-dimensional figure that extends forever in opposite directions.line segment

A line segment is a part of a line that has two endpoints.Parallel

Two or more lines are parallel when they lie in the same plane and never intersect. These lines will always have the same slope.Point

A point is a location in space that does not have size or shape.Point of Intersection

A point of intersection is the point where two intersecting lines meet.Ray

A ray is a part of a line that has one endpoint and continues indefinitely in one direction.Vertex

A vertex is a point of intersection of the lines or rays that form an angle.### Image Attributions

Here you'll learn to identify angles by vertex and ray.