Pythagorean Theorem Proofs Quick Check 1 of 51 of 5 Items Question Which statement explains the Pythagorean Theorem?(1 point) Responses 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. 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 a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
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 angle at point F is 90°. No, because the angle at point cap f is 90 degrees . Yes, because it is a right triangle. Yes, because it is 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 325 is not equal to 144. No, because 325 is not equal to 144. No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 22 is not equal to 15. No, because 22 is not equal to 15. No, because 244 is not equal to 225.
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, 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 leg length of 24. The triangle is a right triangle with a missing leg length of 24. 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.
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 two parts are negated by using the word not. The two parts are negated by using the word not . The converse of a theorem has no relationship to the original theorem.
The if part and the then part switch places.
The correct 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." This means that if you have a right triangle, which is a triangle with one angle measuring 90 degrees, then the square of the length of the two shorter sides (legs) will be equal to the square of the length of the longest side (hypotenuse). So, according to the Pythagorean Theorem, if a, b, and c represent the lengths of the sides of a right triangle, where c is the length of the hypotenuse, then a^2 + b^2 = c^2.
