Explain a Proof of the Pythagorean Theorem and its Converse: CCSS.Math.Content.8.G.B.6 - Common Core: 8th Grade Math
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Which shape does the Pythagorean Theorem apply to?
Which shape does the Pythagorean Theorem apply to?
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:
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:
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How is the Pythagorean Theorem used?
How is the Pythagorean Theorem used?
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.
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.
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What is the formula associated with the Pythagorean Theorem?
What is the formula associated with the Pythagorean Theorem?
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:
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:
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How is the converse of the Pythagorean Theorem used?
How is the converse of the Pythagorean Theorem used?
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.
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.
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Which answer choice provides side lengths of a right triangle?
Which answer choice provides side lengths of a right triangle?
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.
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
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Will the Pythagorean Theorem work to solve for a missing side length of a three sided figure?
Will the Pythagorean Theorem work to solve for a missing side length of a three sided figure?
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:
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:
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If the equation 
is found to be true, what do we know?
If the equation
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
The equation shown in the question,
In this equation:
This means that
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If the equation 
is found to be true, what do we know?
If the equation
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
The equation shown in the question,
In this equation:
This means that
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If the equation 
is found to be true, what do we know?
If the equation
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
The equation shown in the question,
In this equation:
This means that
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If the equation 
is found to be true, what do we know?
If the equation
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
The equation shown in the question,
In this equation:
This means that
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If the equation 
is found to be true, what do we know?
If the equation
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
The equation shown in the question,
In this equation:
This means that
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Can the Pythagorean Theorem be used to solve for the missing side length in the triangle provided?
Can the Pythagorean Theorem be used to solve for the missing side length in the triangle provided?
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 
within the triangle provided in the question.
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
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