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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

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Example Questions

Example Question #394 : Grade 8

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:

$\angle{\ d}$

$\angle{\ h}$

$\angle{\ c}$

$\angle{\ b}$

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.

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.

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Example Question #395 : Grade 8

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:

$\angle{\ f}$

$\angle{\ h}$

$\angle{\ b}$

$\angle{\ c}$

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.

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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:

$\angle{\ d}$

$\angle{\ e}$

$\angle{\ f}$

$\angle{\ h}$

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

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:

$\angle{\ a}$

$\angle{\ c}$

$\angle{\ d}$

$\angle{\ e}$

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 $45^\circ$

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Example Question #1 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

Which shape does the Pythagorean Theorem apply to?

Possible Answers:

Squares

Triangles

Cubes

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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Example Question #81 : Geometry

How is the Pythagorean Theorem used?

Possible Answers:

The Pythagorean Theorem is used to solve for a missing side length of a right triangle

The Pythagorean Theorem is used to solve for the area of a right triangle

The Pythagorean Theorem is used to solve for a missing side length of a triangle

The Pythagorean Theorem is used to solve for the volume of a triangle

Correct answer:

The Pythagorean Theorem is used to solve for a missing side length of a right triangle

Explanation:

The Pythagorean Theorem states that for 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

With this equation, we can solve for a missing side length.

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Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

What is the formula associated with the Pythagorean Theorem?

Possible Answers:

a^2+b^2=c^2

a+b=c

a^2-b^2=c

a^2+b^2=c

a^2-b^2=c^2

Correct answer:

a^2+b^2=c^2

Explanation:

The Pythagorean Theorem states that for 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

In this equation:

$a \textup{ and }b=\textup{legs}$

$c=\textup{hypotenuse}$

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Example Question #82 : Geometry

How is the converse of the Pythagorean Theorem used?

Possible Answers:

To determine if a triangle is a right triangle

To determine the a missing side length of a right triangle

To determine if a shape is in fact a triangle

To determine the a missing side length of a triangle

Correct answer:

To determine if a triangle is a right triangle

Explanation:

The converse of the Pythagorean Theorem is used to determine if a triangle is a right triangle. If we are given three side lengths we can plug them into the Pythagorean Theorem formula:

a^2+b^2=c^2

If the square of the hypotenuse is equal to the sum of the square of the other two sides, then the triangle is a right triangle.

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Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

Will the Pythagorean Theorem work to solve for a missing side length of a three sided figure?

Possible Answers:

No, the Pythagorean Theorem will only work to solve for the missing side length of a right triangle

Yes, the Pythagorean Theorem is used to solve for any missing side length of at three sided figure

Yes, the Pythagorean Theorem is used to solve for any missing side length of a triangle

No, the Pythagorean Theorem will only work to solve for the missing side length of a triangle

Correct answer:

No, the Pythagorean Theorem will only work to solve for the missing side length of a right triangle

Explanation:

The Pythagorean Theorem can only be used to solve for the missing side length of a right triangle. Remember, the Pythagorean Theorem states that for 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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Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation 5^2+12^2=13^2 is found to be true, what do we know?

Possible Answers:

A right triangle has a hypotenuse of and side lengths of and

The Pythagorean Theorem only works if the hypotenuse is an even number

The Pythagorean Theorem only works if the hypotenuse is an odd number

A right triangle has a hypotenuse of 169 and side lengths of and 144

Correct answer:

A right triangle has a hypotenuse of and side lengths of and

Explanation:

The equation shown in the question, 5^2+12^2=13^2 , is the equation for the Pythagorean Theorem:

a^2+b^2=c^2

In this equation:

$a \textup{ and }b=\textup{legs}$

$c=\textup{hypotenuse}$

This means that and are the side lengths and in the hypotenuse of the triangle

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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 #394 : Grade 8

Example Question #395 : Grade 8

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 #1 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

Example Question #81 : Geometry

Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

Example Question #82 : Geometry

Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

All Common Core: 8th Grade Math Resources

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