### All Common Core: 8th Grade Math Resources

## Example Questions

### Example Question #71 : Geometry

The image provided contains a set of parallel lines, and , and a transversal line, . If angle is equal to , then which of the other angles is equal to

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines and are parallel lines and line is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

Angle is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs and as well as angle and .

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are vertical angles; thus, both angle and are congruent and equal

### Example Question #1 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines, and , and a transversal line, . If angle is equal to , then which of the other angles is equal to

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines and are parallel lines and line is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

Angle is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs and as well as angle and .

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are vertical angles; thus, both angle and are congruent and equal

### Example Question #1 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines, and , and a transversal line, . If angle is equal to , then which of the other angles is equal to

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines and are parallel lines and line is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

Angle is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs and as well as angle and .

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are corresponding angles; thus, both angle and are congruent and equal

### Example Question #1 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are corresponding angles; thus, both angle and are congruent and equal

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are alternate exterior angles; thus, both angle and are congruent and equal

### Example Question #2 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are alternate exterior angles; thus, both angle and are congruent and equal

### Example Question #2 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are alternate interior angles; thus, both angle and are congruent and equal

### Example Question #8 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle and are alternate interior angles; thus, both angle and are congruent and equal

The image provided contains a set of parallel lines, and , and a transversal line, . Which angle is **NOT** equal to angle

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle and are vertical angles, which means they are congruent.

Angle and are alternate exterior angles, which means they are congruent.

Angle and are corresponding angles, which means they are congruent.

However, angle and do not share a common angle relationship; thus they are not congruent.

### Example Question #10 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines, and , and a transversal line, . Which angle is **NOT** equal to angle

**Possible Answers:**

**Correct answer:**

First, we need to define some key terms:

**Parallel Lines**: Parallel lines are lines that will never intersect with each other.

**Transversal Line**: A transversal line is a line that crosses two parallel lines.

It is important to know that transversal lines create angle relationships:

- Vertical angles are congruent
- Corresponding angles are congruent
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Let's look at angle in the image provided below to demonstrate our relationships.

Angle and are vertical angles.

Angle and are corresponding angles.

Angle and are exterior angles.

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle and are vertical angles, which means they are congruent.

Angle and are alternate interior angles, which means they are congruent.

Angle and are corresponding angles, which means they are congruent.

However, angle and do not share a common angle relationship; thus they are not congruent.