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

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Example Questions

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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

Cubes

Right triangles

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:

2

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 the area of a right 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 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:

2

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

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:

Correct answer:

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:

In this equation:

2

 

Example Question #4 : 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 right triangle 

To determine the a missing side length of a 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:

 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. 

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

Which answer choice provides side length of a right triangle? 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we use the converse of the Pythagorean Theorem. We will substitute the given side lengths to determine which three side lengths make the formula for Pythagorean Theorem true. It is important to remember that the hypotenuse will always be the longest side length, so the value for  will always be the greatest:

Let's plug in the side lengths into our formula and solve:

 

 

 

This means that a triangle that has side lengths of  is a right triangle. 

Example Question #6 : 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:

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

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

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

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

2

Example Question #7 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation  is found to be true, what do we know?

 

Possible Answers:

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  and side lengths of  and 

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, , is the equation for the Pythagorean Theorem:

In this equation:

2

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



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

If the equation  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 

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

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

Correct answer:

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

Explanation:

The equation shown in the question, , is the equation for the Pythagorean Theorem:

In this equation:

2

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

Example Question #9 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation  is found to be true, what do we know?

 

Possible Answers:

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

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

Correct answer:

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

Explanation:

The equation shown in the question, , is the equation for the Pythagorean Theorem:

In this equation:

2

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


 

Example Question #10 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6

If the equation  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 

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

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

Correct answer:

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

Explanation:

The equation shown in the question, , is the equation for the Pythagorean Theorem:

In this equation:

2

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



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