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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

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 $135^\circ?$

Possible Answers:

$\angle{\ h}$

$\angle{\ f}$

$\angle{\ g}$

$\angle{\ b}$

Correct answer:

$\angle{\ g}$

Explanation:

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 $135^\circ$

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Example Question #3 : 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, $\overline{AB}$ 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 $45^\circ$

Possible Answers:

$\angle{\ c}$

$\angle{\ h}$

$\angle{\ a}$

$\angle{\ g}$

Correct answer:

$\angle{\ h}$

Explanation:

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.

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 $45^\circ$

Report an Error

Example Question #3 : 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, $\overline{AB}$ 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 $135^\circ?$

Possible Answers:

$\angle{\ b}$

$\angle{\ h}$

$\angle{\ e}$

$\angle{\ f}$

Correct answer:

$\angle{\ e}$

Explanation:

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.

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 $135^\circ$

Report an Error

Example Question #4 : 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, $\overline{AB}$ 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 $45^\circ$

Possible Answers:

$\angle{\ g}$

$\angle{\ a}$

$\angle{\ f}$

$\angle{\ e}$

Correct answer:

$\angle{\ f}$

Explanation:

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.

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 $45^\circ$

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Example Question #3 : 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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ g}?$

Possible Answers:

$\angle{\ d}$

$\angle{\ c}$

$\angle{\ a}$

$\angle{\ e}$

Correct answer:

$\angle{\ d}$

Explanation:

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.

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.

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Example Question #4 : 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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ f}?$

Possible Answers:

$\angle{\ c}$

$\angle{\ d}$

$\angle{\ b}$

$\angle{\ h}$

Correct answer:

$\angle{\ c}$

Explanation:

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.

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.

Report an Error

Example Question #6 : 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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ d}?$

Possible Answers:

$\angle{\ c}$

$\angle{\ f}$

$\angle{\ h}$

$\angle{\ b}$

Correct answer:

$\angle{\ c}$

Explanation:

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.

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.

Report an Error

Example Question #11 : 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, $\overline{AB}$ and $\overline{CD}$ , and a transversal line, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ b}?$

Possible Answers:

$\angle{\ f}$

$\angle{\ e}$

$\angle{\ h}$

$\angle{\ d}$

Correct answer:

$\angle{\ e}$

Explanation:

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.

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.

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Example Question #391 : Grade 8

Possible Answers:

$\angle{\ d}$

$\angle{\ a}$

$\angle{\ c}$

$\angle{\ e}$

Correct answer:

$\angle{\ d}$

Explanation:

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.

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 $45^\circ$

Report an Error

Example Question #392 : Grade 8

Which shape does the Pythagorean Theorem apply to?

Possible Answers:

Cubes

Squares

Triangles

Right triangles

Correct answer:

Right triangles

Explanation:

The Pythagorean Theorem applies to right triangles. The Theorem states that for all right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

a^2+b^2=c^2

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

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

Example Question #3 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #3 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #4 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #3 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #4 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #6 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #11 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

Example Question #391 : Grade 8

Example Question #392 : Grade 8

All Common Core: 8th Grade Math Resources

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