Which statement explains the Pythagorean Theorem?
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 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 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 legs is equal to the square of the hypotenuse.
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."
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."
To understand this theorem, we can break it down into its components. A right triangle is a triangle that has one angle measuring 90 degrees. The two sides adjacent to this right angle are called the legs, and the side opposite the right angle is called the hypotenuse. The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
To find out if a triangle is a right triangle, you can check if it satisfies the conditions of having one angle measuring 90 degrees.
To apply the Pythagorean Theorem, you need to know the lengths of the two legs of a right triangle. Let's say the lengths of the legs are a and b, and the length of the hypotenuse is c. The theorem can be written as: a^2 + b^2 = c^2. By substituting the lengths of the legs and the hypotenuse into this equation, you can determine if the theorem holds true for a particular right triangle.