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

## 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?

Squares

Cubes

Right triangles

Triangles

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:

### 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?

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

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:

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?

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:

### 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?

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

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?

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?

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

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:

### 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?

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

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:

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?

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

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:

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?

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

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:

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?

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

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:

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

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