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 #85 : Geometry
Which shape does the Pythagorean Theorem apply to?
Right triangles
Squares
Triangles
Cubes
Right triangles
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 #1 : 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 the volume 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 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 a missing side length of a right triangle
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 #87 : Geometry
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:
Example Question #88 : Geometry
How is the converse of the Pythagorean Theorem used?
To determine the a missing side length of a right triangle
To determine if a triangle is a right triangle
To determine the a missing side length of a triangle
To determine if a shape is in fact a triangle
To determine if a 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.
Example Question #89 : Geometry
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
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
No, the Pythagorean Theorem will only work to solve for the missing side length of a right triangle
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 #2 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6
If the equation 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an even number
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
A right triangle has a hypotenuse of
The equation shown in the question, 
In this equation:
This means that 
Example Question #7 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6
If the equation 
The Pythagorean Theorem only works if the hypotenuse is an even number
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
A right triangle has a hypotenuse of
The equation shown in the question, 
In this equation:
This means that 
Example Question #3 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6
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
A right triangle has a hypotenuse of
The equation shown in the question, 
In this equation:
This means that 
Example Question #4 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6
If the equation 
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an odd number
A right triangle has a hypotenuse of 
The Pythagorean Theorem only works if the hypotenuse is an even number
A right triangle has a hypotenuse of
The equation shown in the question, 
In this equation:
This means that 
Example Question #5 : Explain A Proof Of The Pythagorean Theorem And Its Converse: Ccss.Math.Content.8.G.B.6
If the equation 
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
A right triangle has a hypotenuse of 
A right triangle has a hypotenuse of
The equation shown in the question, 
In this equation:
This means that 
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