Which statement explains the Pythagorean Theorem?
a: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.
b:If all angles in a triangle are of equal measure, then the length of all sides will be equal.
c: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.
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.
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.
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.
Explanation: The Pythagorean Theorem is a fundamental principle in Euclidean geometry that relates the lengths of the sides of a right triangle. In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. According to the Pythagorean Theorem, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.