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Common Core: 8th Grade Math : Geometry

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 #11 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation?

Possible Answers:

Yes, transformation

Yes, dilation

Yes, both a transformation and dilation

Correct answer:

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation.

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape.

Transformation: A transformation can be described in three ways:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.

The yellow rectangle is smaller than the blue rectangle, but a dilation did not occur because because the scale factor for the length and the width are not equal to each other; thus, the shapes are not similar.

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Example Question #12 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation?

Possible Answers:

Yes, both a transformation and dilation

Yes, dilation

Yes, transformation

Correct answer:

Explanation:

Let's recall our key terms:

Transformation: A transformation can be described in three ways:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.

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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, $\overline{AB}$ 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:

$\angle{\ f}$

$\angle{\ c}$

$\angle{\ b}$

$\angle{\ d}$

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.

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 $135^\circ$

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Example Question #71 : Geometry

Possible Answers:

$\angle{\ e}$

$\angle{\ f}$

$\angle{\ h}$

$\angle{\ b}$

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 $\angle{\ a}$ . 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 $135^\circ$

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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, $\overline{AB}$ 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:

$\angle{\ f}$

$\angle{\ c}$

$\angle{\ g}$

$\angle{\ e}$

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 $\angle{\ b}$ . 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 $45^\circ$

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Example Question #391 : Grade 8

Possible Answers:

$\angle{\ g}$

$\angle{\ f}$

$\angle{\ b}$

$\angle{\ h}$

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.

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 #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:

$\angle{\ g}$

$\angle{\ h}$

$\angle{\ c}$

$\angle{\ a}$

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 $45^\circ$

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Example Question #392 : Grade 8

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:

$\angle{\ b}$

$\angle{\ e}$

$\angle{\ h}$

$\angle{\ f}$

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 $135^\circ$

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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, $\overline{EF}$ . If angle $\angle{\ d}$ is equal to $45^\circ$ , then which of the other angles is equal to $45^\circ$

Possible Answers:

$\angle{\ g}$

$\angle{\ f}$

$\angle{\ e}$

$\angle{\ a}$

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 #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, $\overline{EF}$ . Which angle is NOT equal to angle $\angle {\ g}?$

Possible Answers:

$\angle{\ e}$

$\angle{\ c}$

$\angle{\ d}$

$\angle{\ a}$

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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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : Geometry

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

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #11 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Example Question #12 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

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

Example Question #71 : Geometry

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

Example Question #391 : Grade 8

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 #392 : Grade 8

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

All Common Core: 8th Grade Math Resources

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