Which statement explains the Pythagorean Theorem?(1 point)
Responses
If all angles in a triangle are of equal measure, then the length of all sides will be equal.
If all angles in a triangle are of equal measure, then the length of all sides will be equal.
If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.
If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.
If the interior angles of a triangle add up to 180°, then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If the interior angles of a triangle add up to 180 degrees , then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
Pythagorean Theorem Proofs Quick Check
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Question
Use the image to answer the question.
A triangle has the vertices labeled upper E upper F upper D. The height upper E upper F is labeled 15, the base upper D upper F is labeled 20, and the hypotenuse upper D upper E is labeled 25. Angle upper E measures 60 degrees and angle upper D measures 30 degrees.
Does the Pythagorean Theorem apply to this triangle? How do you know?
(1 point)
Responses
Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle
No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.
Yes, because it is a right triangle.
Yes, because it is a right triangle.
No, because the angle at point F is 90°.
No, because the triangle is not a right triangle.
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
Responses
No, because 22 is not equal to 15.
No, because 22 is not equal to 15.
No, because 244 is not equal to 225.
No, because 244 is not equal to 225.
No, because 369 is not equal to 100.
No, because 369 is not equal to 100.
No, because 325 is not equal to 144.
No, the lengths 15, 10, and 12 do not satisfy the equation a^2 + b^2 = c^2.
is it
No, because 22 is not equal to 15.
or
No, because 244 is not equal to 225.
or
No, because 369 is not equal to 100.
or
No, because 325 is not equal to 144.
No, it is not any of those options. The correct explanation is:
No, because the lengths 15, 10, and 12 do not satisfy the equation a^2 + b^2 = c^2.
I can't use that
Apologies for the confusion. In that case, the correct response would be:
No, because 22^2 is not equal to 15^2 + 10^2.