Explain a Proof of the Pythagorean Theorem and its Converse: CCSS.Math.Content.8.G.B.6
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8th Grade Math › Explain a Proof of the Pythagorean Theorem and its Converse: CCSS.Math.Content.8.G.B.6
Which answer choice provides side lengths 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 
Let's plug in the side lengths into our formula and solve:
This means that a triangle that has side lengths of 
Can the Pythagorean Theorem be used to solve for the missing side length in the triangle provided?
No because the triangle is not a right triangle
No because the triangle doesn't provide enough information
Yes because the triangle is a right triangle
Yes because the triangle is only missing one side length
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:
However, the triangle provided is not a right triangle because there is not an angle that is equal to 
Will the Pythagorean Theorem work to solve for a missing side length of a three sided figure?
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 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
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:
If the equation 
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
The Pythagorean Theorem only works if the hypotenuse is an even number
Explanation
The equation shown in the question, 
In this equation:
This means that 
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:
If the equation 
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
The Pythagorean Theorem only works if the hypotenuse is an even number
Explanation
The equation shown in the question, 
In this equation:
This means that 
How is the converse of the Pythagorean Theorem used?
To determine if a triangle is a right triangle
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 shape is in fact a 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.
If the equation 
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
The Pythagorean Theorem only works if the hypotenuse is an even number
Explanation
The equation shown in the question, 
In this equation:
This means that 
If the equation 
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
The Pythagorean Theorem only works if the hypotenuse is an even number
Explanation
The equation shown in the question, 
In this equation:
This means that 
If the equation 
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an even number
The Pythagorean Theorem only works if the hypotenuse is an odd number
Explanation
The equation shown in the question, 
In this equation:
This means that 
