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.
Pythagorean Theorem Proofs Quick Check
2 of 52 of 5 Items
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
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
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.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 244 is not equal to 225.
No, because 244 is not equal to 225.
No, because 22 is not equal to 15.
No, because 22 is not equal to 15.
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, because 325 is not equal to 144.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 side of 34.99.
The triangle is a right triangle with a missing side of 34.99.
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.What is a converse of a theorem that is an if-then statement?(1 point)
Responses
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 converse is the same as the original theorem.
The converse is the same as the original theorem.
The two parts are negated by using the word not.
The two parts are negated by using the word not .
The if part and the then part switch places. please answer them all
Some were wrong here are the correct answers:
1. B.) 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. C.) Yes, because it is a right triangle.
3. C.) No, because 244 is not equal to 225.
4. B.) The triangle is a right triangle with a missing leg length of 24.
5. The if part and the then part switches places.
The statement that explains the Pythagorean Theorem is: "If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse."
For the second question, the Pythagorean Theorem does apply to the given triangle because it is a right triangle. The correct answer is: "Yes, because it is a right triangle."
For the third question, to determine if a triangle with sides 15, 10, and 12 is a right triangle, you can use the Converse of the Pythagorean Theorem. By checking if 152 + 102 = 122, you can determine that it is not a right triangle. The correct answer is: "No, because 225 is not equal to 244."
For the fourth question, if the equation 182 + b2 = 302 is found to be true, it means that the triangle is a right triangle with legs measuring 18 and b, and the hypotenuse is 30. The correct answer is: "The triangle is a right triangle, and the legs are 30 and 24."
Lastly, the converse of a theorem is when the if part and the then part switch places. The correct answer is: "The if part and the then part switch places."
can you double check to make sure?
double check 2 and 4 please
Apologies for the confusion earlier. Upon double-checking:
2. The Pythagorean Theorem does not apply to the given triangle because it is not a right triangle. The correct answer is: "No, because the triangle is not a right triangle."
4. If the equation 182 + b2 = 302 is found to be true, it means that the triangle is a right triangle with legs measuring 18 and b, and the hypotenuse is 30. The correct answer is: "The triangle is a right triangle, and the legs are 18 and 24."
I apologize again for any previous incorrect information provided.
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 side of 34.99.
The triangle is a right triangle with a missing side of 34.99.
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.
Apologies for the confusion earlier. I appreciate your patience. Upon reviewing the question again:
If the equation 182 + b2 = 302 is found to be true, it means that the triangle is a right triangle, and the legs are 18 and b, with the hypotenuse being 30.
The correct answer is: "The triangle is a right triangle, and the legs are 18 and b, with the hypotenuse being 30."
Thank you for bringing this to my attention, and I apologize for any previous incorrect information provided.
choose from the options i gave you please 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 side of 34.99.
The triangle is a right triangle with a missing side of 34.99.
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.
Apologies for the confusion. Among the options you provided, the correct answer is:
"The triangle is a right triangle, and the hypotenuse is 18."
1. The statement that explains the Pythagorean Theorem is: If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
To get this answer, you can remember that the Pythagorean Theorem specifically pertains to right triangles. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
2. The Pythagorean Theorem applies to a triangle if it is a right triangle. You can determine if a triangle is a right triangle by checking if one of its angles measures 90 degrees.
In the given triangle with vertices labeled E, F, and D, if the angle at point F is 90°, then the triangle is a right triangle. Therefore, the correct response is: No, because the angle at point F is 90°.
3. To determine if a triangle with sides 15, 10, and 12 is a right triangle, you can use the Converse of the Pythagorean Theorem. The Converse states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
In this case, calculating the squares of the sides, we get 225, 100, and 144. Since 225 + 100 = 325, and 325 is not equal to 144, the Converse of the Pythagorean Theorem is not satisfied. Therefore, the correct response is: No, because 325 is not equal to 144.
4. If the equation 182 + b^2 = 302 is found to be true, we can conclude that the triangle is a right triangle, and the legs are 30 and 24.
To solve for b, you can subtract 182 from both sides of the equation, resulting in b^2 = 302 - 182, which simplifies to b^2 = 120. Taking the square root of both sides gives you b = √120, which can further simplify to b = 2√30.
Therefore, the correct response is: The triangle is a right triangle, and the legs are 30 and 24.
5. The converse of a theorem that is an if-then statement is when the if part and the then part switch places.
For example, if the original theorem is "If a triangle has three equal sides, then it is an equilateral triangle," the converse of this theorem would be "If a triangle is an equilateral triangle, then it has three equal sides."
Therefore, the correct response is: The if part and the then part switch places.