# Basic Geometry : Plane Geometry

## Example Questions

### Example Question #1 : How To Find A Ray

Which of the following are the sides of  ?

and

and

and

and

and

and

Explanation:

The sides of an angle are two rays, both of which begin at a common vertex. Since the middle letter of the name of this angle is  is the common endpoint; therefore, the name of each ray starts with . This makes  and  the correct choice.

Note that  and  cannot be correct: these are line segments.

### Example Question #1 : How To Find A Ray

A ray is different from a line in that

A line can be curved but a ray is always straight

A ray can cross itself

A line has a beginning and a ray does not

One side of the ray goes on forever while the other stops

One side of the ray goes on forever while the other stops

Explanation:

A ray is defined by two points, one that defines the beginning, and the other that defines the direction - this ray goes on forever in whatever direction is defined by that second point

### Example Question #2 : How To Find A Ray

Which of the following is not a side of ?

Explanation:

The two sides of an angle are the two rays that compose it. Each of these rays begins at the vertex and proceeds out from there. In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is , each of our rays must begin with . Only  fails to do so.

### Example Question #4 : How To Find A Ray

How does a ray differ from a line segment?

A line segment continues in both directions, a ray only continues in one direction.

A line segments connects to itself forming a shape, a ray does not.

A ray has two end points whereas a line segment only has one.

Ray has two end points.

A line segment has two end points, a ray only has one.

A line segment has two end points, a ray only has one.

Explanation:

Line segment: part of a line that has two distinct end points.

Ray: portion of a line with one end point, where the other end of the line continues to infinity.

### Example Question #2 : How To Find A Ray

Refer to the above diagram. The plane containing the above figure can be called Plane .

False

True

False

Explanation:

A plane can be named after any three points on the plane that are not on the same line. As seen below, points ,  and  are on the same line.

Therefore, Plane  is not a valid name for the plane.

### Example Question #6 : How To Find A Ray

Refer to the above diagram.

True or false:  can also be called .

False

True

False

Explanation:

A line segment has two letters in its name, each of which is an endpoint.  is therefore the segment marked in red below.

is not a valid name, since  is not an endpoint of the segment.

### Example Question #3 : How To Find A Ray

Refer to the above diagram.

True or false:  can also be called .

False

True

False

Explanation:

A segment is named with only two letters, each of which is an endpoint.  is not a valid name.

### Example Question #8 : How To Find A Ray

Refer to the above diagram.

True or false:  and  refer to the same line segment.

False

True

True

Explanation:

The two letters in the name of a line segment are its endpoints in either order. Therefore,  is the segment with endpoints  and ; consequently, it can also be called .

### Example Question #2 : How To Find A Ray

Refer to the above diagram.

True or false:  and  refer to the same ray.

True

False

False

Explanation:

A ray is named with two letters, the first of which is an endpoint and the second of which is any other point the ray passes through.  is a ray with endpoint , and  is a ray with endpoint  and  are therefore not the same ray.

### Example Question #10 : How To Find A Ray

Refer to the above diagram.

True or false:  and  refer to the same ray.

True

False