### All Basic Geometry Resources

## Example Questions

### Example Question #1592 : Basic Geometry

Refer to the above diagram.

True or false: and comprise a linear pair.

**Possible Answers:**

True

False

**Correct answer:**

False

By definition, two angles form a linear pair if and only if

(1) they have the same vertex;

(2) they share a side; and,

(3) their interiors have no points in common.

is the angle with vertex ; its two sides are the rays and , which have endpoint and pass through and , respectively. has the same vertex; its two sides are the rays and , which have endpoint and pass through and , respectively. and are indicated below in red and green, respectively:

The angles have the same vertex and they share a side. However, the interior of is entirely contained in the interior of . The angles do not comprise a linear pair.

### Example Question #1591 : Plane Geometry

Refer to the above diagram.

True or false: Quadrilateral can also be called Quadrilateral .

**Possible Answers:**

True

False

**Correct answer:**

True

A quadrilateral is named after its four vertices in consecutive order, going clockwise or counterclockwise. Quadrilateral is the figure in red, below:

, , , and also name the four vertices in clockwise order. It follows that Quadrilateral is another valid name for the figure.

### Example Question #1592 : Plane Geometry

Refer to the above diagram.

True or false: Quadrilateral can also be called Quadrilateral .

**Possible Answers:**

True

False

**Correct answer:**

True

A quadrilateral is named after its four vertices in consecutive order, going clockwise or counterclockwise. Quadrilateral is the figure in red, below:

, , , and name the four vertices in counterclockwise order. It follows that Quadrilateral is another valid name for the figure.

### Example Question #1593 : Plane Geometry

Refer to the above diagram. .

True, false, or inconclusive:

**Possible Answers:**

Inconclusive

False

True

**Correct answer:**

Inconclusive

and form a pair of vertical angles, and are consequently congruent whether or not it holds that . Therefore, whether the lines are parallel cannot be determined.

### Example Question #1594 : Plane Geometry

Figure NOT drawn to scale.

Refer to the above diagram. .

True, false, or inconclusive: .

**Possible Answers:**

True

False

Inconclusive

**Correct answer:**

True

and are both inside the two lines and , and they appear on opposite sides of transversal . They are thus alternate interior angles, by definition, and since they are congruent, then by the Converse of the Alternate Interior Angles Theorem, it follows that ,

### Example Question #1595 : Plane Geometry

Refer to the above diagram.

True or false: and refer to the same triangle.

**Possible Answers:**

True

False

**Correct answer:**

True

The letters in the name of a triangle name its vertices, so refers to the triangle with vertices , , and . A triangle is named after its vertices in any order, so this triangle can also be called .

### Example Question #1596 : Plane Geometry

Figure NOT drawn to scale.

Refer to the above diagram.

and are supplementary.

True, false, or inconclusive: It follows that .

**Possible Answers:**

Inconclusive

True

False

**Correct answer:**

Inconclusive

and form a linear pair of angles and are supplementary regardless of whether or not .

### Example Question #1597 : Plane Geometry

Figure NOT drawn to scale.

Refer to the above diagram.

True, false, or inconclusive: it follows that

**Possible Answers:**

False

True

Inconclusive

**Correct answer:**

True

and form a linear pair of angles, and are therefore supplementary; the same holds for and . Angles that are supplementary to congruent angles are themselves congruent, so, since , it follows that .

### Example Question #1598 : Plane Geometry

If lines A and B are parallel, what is the measurement of ?

**Possible Answers:**

**Correct answer:**

Notice that and are corresponding angles. This means that they possess the same angular measurements; thus, we can write the following:

Now, notice that and the provided angle of angle are vertical angles. Vertical angles share the same angle measurements; therefore, we may write the following:

If and , then

### Example Question #11 : Geometry

Angle measures

is the bisector of

is the bisector of

What is the measure of ?

**Possible Answers:**

**Correct answer:**

Let's begin by observing the larger angle. is cut into two 10-degree angles by . This means that angles and equal 10 degrees. Next, we are told that bisects , which creates two 5-degree angles. consists of , which is 10 degrees, and , which is 5 degrees. We need to add the two angles together to solve the problem.

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