Pythagorean Theorem Proofs Quick Check

1. 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 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 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 a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.

2. 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

No, because the angle at point F is 90°.
No, because the angle at point cap f is 90 degrees .

Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle

Yes, because it is a right triangle.
Yes, because it is a right triangle.

No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.

3. 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 325 is not equal to 144.
No, because 325 is not equal to 144.

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.

4. If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)
Responses

The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.

The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle with a missing leg length of 24.

The triangle is a right triangle, and the legs are 30 and 24.
The triangle is a right triangle, and the legs are 30 and 24.

The triangle is a right triangle with a missing side of 34.99.

5. What is a converse of a theorem that is an if-then statement?(1 point)
Responses

The converse is the same as the original theorem.
The converse is the same as the original theorem.

The if part and the then part switch places.
The if part and the then part switch places.

The converse of a theorem has no relationship to the original theorem.
The converse of a theorem has no relationship to the original theorem.

The two parts are negated by using the word not.
The two parts are negated by using the word not .