The first letter in the name of a ray always refers to the endpoint of the ray. Therefore,

has its endpoint at and has its endpoint at . The two rays are not opposite rays.You are watching: What are opposite rays in geometry

Refer to the above figure.

True or false:

and comprise a pair of opposite rays.Explanation:

The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray.

and are rays that have endpoint and pass through and , respectively. Those rays are indicated below in red and green, respectively.As it turns out, the two rays are one and the same.

Refer to the above figure.

True or false:

and comprise a pair of opposite rays.Explanation:

Two rays are opposite rays, by definition, if

(1) they have the same endpoint, and

(2) their union is a line.

The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray.

and both have endpoint , so the first criterion is met. passes through point and passes through point ; and are indicated below in green and red, respectively:The union of the two rays is a line. Both criteria are met, so the rays are indeed opposite.

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### Example Question #1544 : Basic Geometry

Refer to the above diagram.

True or false:

, , and are collinear points.**Possible Answers:**

True

False

**Correct answer:**

False

Explanation:

Three points are collinear if there is a single line that passes through all three. In the diagram below, it can be seen that the line that passes through

and does not pass through .

Therefore, the three points are not collinear.

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### Example Question #1545 : Basic Geometry

Refer to the above diagram.

True or false:

, , and are collinear points.**Possible Answers:**

True

False

**Correct answer:**

True

Explanation:

Three points are collinear if there is a single line that passes through all three. In the diagram below, it can be seen that such a line exists.

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### Example Question #1546 : Basic Geometry

True or false: The plane containing the above figure can be called Plane

.**Possible Answers:**

False

True

**Correct answer:**

True

Explanation:

A plane can be named after any three points on the plane that are not on the same line.

, , and do not appear on the same line; for example, as can be seen below, the line that passes through and does not pass through .Plane

is a valid name for the plane that includes this figure.Report an Error

### Example Question #1541 : Plane Geometry

Refer to the above diagram.

True or false: Quadrilateral

can also be called Quadrilateral .**Possible Answers:**

True

False

**Correct answer:**

False

Explanation:

A quadrilateral is named after its four vertices in consecutive order, going clockwise or counterclockwise. Quadrilateral

is the figure in red, below:, , , and are not a clockwise or counterclockwise ordering of the vertices, so Quadrilateral is not a valid name for the quadrilateral.Report an Error

### Example Question #1548 : Basic Geometry

Refer to the above diagram:

True or false:

may also called .**Possible Answers:**

False

True

**Correct answer:**

False

Explanation:

A line can be named after any two points it passes through. The line

is indicated in green below.The line does not pass through

, so cannot be part of the name of the line. Specifically, is not a valid name.Report an Error

### Example Question #1549 : Basic Geometry

Examine the diagram. Which of these conditions does *not* prove that

**Possible Answers:**

and

Any of these statements can be used to prove that

.**Correct answer:**

Explanation:

If

and , then , since two lines parallel to the same line are parallel to each other.If

, then , since two same-side interior angles formed by transversal are supplementary.If

, then , since two alternate interior angles formed by transversal are congruent.However,

regardless of whether and are parallel; they are vertical angles, and by the Vertical Angles Theorem, they*must*be congruent.

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### Example Question #1 : How To Find An Angle Of A Line

An isosceles triangle has an interior angle that measures

. What are the measures of its other two angles?**Possible Answers:**

This triangle cannot exist.

**Correct answer:**

Explanation:

By the Isosceles Triangle Theorem, two interior angles must be congruent. However, since a triangle cannot have two obtuse interior angles, the two missing angles must be the ones that are congruent. Since the total angle measure of a triangle is

, each of the missing angles measures .See more: Is There Gluten In Reese'S Peanut Butter Cups Gluten, Gluten Free

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