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Common Core: 8th Grade Math : Explain a Proof of the Pythagorean Theorem and its Converse: CCSS.Math.Content.8.G.B.6

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Example Questions

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:

Right triangles

Cubes

Triangles

Squares

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

How is the Pythagorean Theorem used?

Possible Answers:

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

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 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 #1 : 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

a^2+b^2=c^2

a^2-b^2=c^2

a^2-b^2=c

a+b=c

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

How is the converse of the Pythagorean Theorem used?

Possible Answers:

To determine the a missing side length of a triangle

To determine the a missing side length of a right triangle

To determine if a triangle is a right triangle

To determine if a shape is in fact 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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Example Question #5 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation 3^2+4^2=5^2 is found to be true, what do we know?

Possible Answers:

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

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

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

Correct answer:

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

Explanation:

The equation shown in the question, 3^2+4^2=5^2 , 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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Example Question #6 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation 6^2+8^2=10^2 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 odd number

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

A right triangle has a hypotenuse of 100 and side lengths of and

Correct answer:

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

Explanation:

The equation shown in the question, 6^2+8^2=10^2 , 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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Example Question #7 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation 8^2+15^2=17^2 is found to be true, what do we know?

Possible Answers:

A right triangle has a hypotenuse of 289 and side lengths of and 225

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

Correct answer:

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

Explanation:

The equation shown in the question, 8^2+15^2=17^2 , 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

Report an Error

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

If the equation 2.1^2+7.2^2=7.5^2 is found to be true, what do we know?

Possible Answers:

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

A right triangle has a hypotenuse of 7.5 and side lengths of 2.1 and 7.2

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

A right triangle has a hypotenuse of 56.25 and side lengths of 4.41 and 51.84

Correct answer:

A right triangle has a hypotenuse of 7.5 and side lengths of 2.1 and 7.2

Explanation:

The equation shown in the question, 2.1^2+7.2^2=7.5^2 , 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 2.1 and 7.2 are the side lengths and 7.5 in the hypotenuse of the triangle

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Common Core: 8th Grade Math : Explain a Proof of the Pythagorean Theorem and its Converse: CCSS.Math.Content.8.G.B.6

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

All Common Core: 8th Grade Math Resources

Example Questions

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

Example Question #2 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

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

Example Question #2 : 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

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

Example Question #5 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

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

Example Question #7 : 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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