which statement explains the Pythagorean Theorem?
A. 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.
B. If all angles in a triangle are of equal measure, then the length of all sides will be equal.
C. 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.
D. If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
D. If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
are you sure?
Yes, I am sure. The correct statement that explains the Pythagorean Theorem is D. 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 theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A. No, because 244 is not equal to 225.
B. No, because 369 is not equal to 100.
C. No, because 325 is not equal to 144.
D. No, because 22 is not equal to 15.
To determine whether a triangle with sides of 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. The Converse states that 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.
Calculating the squares of the sides:
15^2 = 225
10^2 = 100
12^2 = 144
The Converse of the Pythagorean Theorem states that if 225 (the square of the longest side) is equal to 100 + 144 (the sum of the squares of the other two sides), then the triangle is a right triangle.
Since 225 is not equal to 244, 369, or 325, the triangle with sides 15, 10, and 12 is not a right triangle.
The correct answer is C. No, because 325 is not equal to 144.
If the equation 18^(2) + b^(2) = 30^(2) is found to be true, what do we know about the triangle?
A. The triangle is a right triangle with a missing leg length of 24.
B. The triangle is a right triangle, and the hypotenuse is 18.
C. The triangle is a right triangle, with a missing side of 34.99.
D. The triangle is a right triangle, and the legs are 30 and 24.
To determine what we know about the triangle based on the equation 18^2 + b^2 = 30^2, we can use the Pythagorean Theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the legs (non-hypotenuse sides) is equal to the square of the length of the hypotenuse.
Calculating the squares:
18^2 = 324
30^2 = 900
The equation 324 + b^2 = 900 simplifies to b^2 = 900 - 324, which becomes b^2 = 576.
Taking the square root of both sides, we find that b = 24.
Therefore, we know that the triangle is a right triangle with a missing leg length of 24.
The correct answer is A. 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?
A. The *if* part and the *then* part switch places.
B. The converse of a theorem has no relationship to the original theorem.
C. The two parts are negated by using the word not.
D. The converse is the same as the original theorem.
A. The *if* part and the *then* part switch places.
Correct answers:
1) D. 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) A. Yes, because it is a right triangle.
3) A. No, because 244 is not equal to 225.
4) A. The triangle is a right triangle with a missing leg length of 24.
5) A. The *if* part and the *then* part switch places.