Use Informal Arguments to Establish Facts about the Angle Sum and Exterior Angle of Triangles: CCSS.Math.Content.8.G.A.5 - 8th Grade Math

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Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles; thus, both angle $\angle{\ a}$ and $\angle{\ c}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$ ?

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ d}$ are vertical angles; thus, both angle $\angle{\ b}$ and $\angle{\ d}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles; thus, both angle $\angle{\ a}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ f}$ are corresponding angles; thus, both angle $\angle{\ b}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ g}$ are alternate exterior angles; thus, both angle $\angle{\ a}$ and $\angle{\ g}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ h}$ are alternate exterior angles; thus, both angle $\angle{\ b}$ and $\angle{\ h}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ c}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ c}$ . Based on our answer choices, angle $\angle{\ c}$ and $\angle{\ e}$ are alternate interior angles; thus, both angle $\angle{\ c}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ d}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ d}$ . Based on our answer choices, angle $\angle{\ d}$ and $\angle{\ f}$ are alternate interior angles; thus, both angle $\angle{\ d}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ g}?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

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

Angle $\angle{\ g}$ and $\angle{\ e}$ are vertical angles, which means they are congruent.

Angle $\angle{\ g}$ and $\angle{\ a}$ are alternate exterior angles, which means they are congruent.

Angle $\angle{\ g}$ and $\angle{\ c}$ are corresponding angles, which means they are congruent.

However, angle $\angle{\ g}$ and $\angle{\ d}$ do not share a common angle relationship; thus they are not congruent.

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ f}?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

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

Angle $\angle {\ f}$ and $\angle{\ h}$ are vertical angles, which means they are congruent.

Angle $\angle {\ f}$ and $\angle{\ d}$ are alternate interior angles, which means they are congruent.

Angle $\angle {\ f}$ and $\angle{\ b}$ are corresponding angles, which means they are congruent.

However, angle $\angle {\ f}$ and $\angle{\ c}$ do not share a common angle relationship; thus they are not congruent.

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ d}?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

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

Angle $\angle{\ d}$ and $\angle{\ b}$ are vertical angles, which means they are congruent.

Angle $\angle{\ d}$ and $\angle{\ f}$ are alternate interior angles, which means they are congruent.

Angle $\angle{\ d}$ and $\angle{\ h}$ are corresponding angles, which means they are congruent.

However, angle $\angle{\ d}$ and $\angle{\ c}$ do not share a common angle relationship; thus they are not congruent.

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ b}?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

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

Angle $\angle{\ b}$ and $\angle{\ d}$ are vertical angles, which means they are congruent.

Angle $\angle{\ b}$ and $\angle{\ h}$ are alternate exterior angles, which means they are congruent.

Angle $\angle{\ b}$ and $\angle{\ f}$ are corresponding angles, which means they are congruent.

However, angle $\angle{\ b}$ and $\angle{\ e}$ do not share a common angle relationship; thus they are not congruent.

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles; thus, both angle $\angle{\ a}$ and $\angle{\ c}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$ ?

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ d}$ are vertical angles; thus, both angle $\angle{\ b}$ and $\angle{\ d}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles; thus, both angle $\angle{\ a}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ f}$ are corresponding angles; thus, both angle $\angle{\ b}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ a}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ a}$ . Based on our answer choices, angle $\angle{\ a}$ and $\angle{\ g}$ are alternate exterior angles; thus, both angle $\angle{\ a}$ and $\angle{\ g}$ are congruent and equal $135^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ b}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ b}$ . Based on our answer choices, angle $\angle{\ b}$ and $\angle{\ h}$ are alternate exterior angles; thus, both angle $\angle{\ b}$ and $\angle{\ h}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ c}$ is equal to $135^\circ$ , then which of the other angles is equal to $135^\circ?$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ c}$ . Based on our answer choices, angle $\angle{\ c}$ and $\angle{\ e}$ are alternate interior angles; thus, both angle $\angle{\ c}$ and $\angle{\ e}$ are congruent and equal $135^\circ$

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Question

The image provided contains a set of parallel lines, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . If angle $\angle{\ d}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

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 $\overline{AB}$ and $\overline{CD}$ are parallel lines and line $\overline{EF}$ 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 $\angle{\ a}$ in the image provided below to demonstrate our relationships.

Angle $\angle{\ a}$ and $\angle{\ c}$ are vertical angles.

Angle $\angle{\ a}$ and $\angle{\ e}$ are corresponding angles.

Angle $\angle{\ a}$ and $\angle{\ g}$ are exterior angles.

Angle $\angle{\ a}$ is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs $\angle{\ e}$ and $\angle{\ c}$ as well as angle $\angle{\ d}$ and $\angle{\ f}$ .

For this problem, we want to find the angle that is congruent to angle $\angle{\ d}$ . Based on our answer choices, angle $\angle{\ d}$ and $\angle{\ f}$ are alternate interior angles; thus, both angle $\angle{\ d}$ and $\angle{\ f}$ are congruent and equal $45^\circ$

Compare your answer with the correct one above

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