### All Basic Geometry Resources

## Example Questions

### Example Question #11 : How To Find A Ray

Refer to the above figure.

True or false: and comprise a pair of opposite rays.

**Possible Answers:**

False

True

**Correct answer:**

False

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 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.

### Example Question #12 : How To Find A Ray

Refer to the above figure.

True or false: and comprise a pair of opposite rays.

**Possible Answers:**

False

True

**Correct answer:**

False

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.

### Example Question #11 : Transformation

Refer to the above figure.

True or false: and comprise a pair of opposite rays.

**Possible Answers:**

True

False

**Correct answer:**

True

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.

### Example Question #14 : How To Find A Ray

Refer to the above diagram.

True or false: , , and are collinear points.

**Possible Answers:**

False

True

**Correct answer:**

False

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.

### Example Question #12 : How To Find A Ray

Refer to the above diagram.

True or false: , , and are collinear points.

**Possible Answers:**

False

True

**Correct answer:**

True

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.

### Example Question #11 : How To Find A Ray

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

**Possible Answers:**

True

False

**Correct answer:**

True

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.

### Example Question #12 : Lines

Refer to the above diagram.

True or false: Quadrilateral can also be called Quadrilateral .

**Possible Answers:**

True

False

**Correct answer:**

False

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.

### Example Question #1541 : Basic Geometry

Refer to the above diagram:

True or false: may also called .

**Possible Answers:**

True

False

**Correct answer:**

False

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.

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

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

**Possible Answers:**

Any of these statements can be used to prove that .

and

**Correct answer:**

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.

### 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:**

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 .

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