Which statement explains the Pythagorean Theorem?(1 point) Responses 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 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 lengths of the two legs is equal to the square of the length of the hypotenuse.
The statement that explains the Pythagorean Theorem is: "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."
The second statement correctly explains the Pythagorean Theorem: "If a triangle is a right triangle, then the sum of the squares of the two legs is equal to the square of the hypotenuse."
To understand and apply the Pythagorean Theorem, follow these steps:
1. Identify the right triangle: Look for a triangle that has one angle measuring 90 degrees (a right angle).
2. Label the sides: Identify the two sides that form the right angle and label them as the "legs" of the triangle. Label the remaining side as the "hypotenuse."
3. Square the lengths: Take the lengths of the two legs and square them by multiplying each number by itself.
4. Add the squared lengths: Add the values of the squared legs together.
5. Square the hypotenuse: Take the length of the hypotenuse and square it by multiplying it by itself.
6. Compare the values: Check if the sum of the squared legs is equal to the square of the hypotenuse. If they are equal, the triangle satisfies the Pythagorean Theorem.
Remember that the Pythagorean Theorem is applicable only to right triangles, and it helps determine the relationship between the lengths of their sides.
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 F is 90 degrees
no because the triangle is not a right triangle
yes because you can use the pythagoren theorem on any triangle yes because it is a right triangle
The correct response is: No, because the triangle is not a right triangle. The Pythagorean Theorem only applies to right triangles, which have one angle measuring 90 degrees.
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point) No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 244 is not equal to 225.No, because 325 is not equal to 144. No, because 325 is not equal to 144. No, because 22 is not equal to 15.
To determine if the triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. According to the converse, if the square of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Let's check if this condition holds true for the given triangle:
Longest side: 15
Other sides: 10 and 12
15^2 = 225
10^2 + 12^2 = 100 + 144 = 244
Since 225 is not equal to 244, the triangle with sides 15, 10, and 12 is not a right triangle.
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 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 the triangle is a right triangle with a missing leg length of 24.
If the equation 182 + b^2 = 302 is found to be true, we can use it to determine information about the triangle.
By rearranging the equation, we get b^2 = 302 - 182 = 120.
Now, if we take the square root of both sides, we get b = √120 = 10√3.
Therefore, if this equation is true, we know that the triangle is a right triangle, and one of the legs has a length of 10√3.