Which statement explains the Pythagorean Theorem?(1 point)
Responses
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 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 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 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.
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 Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written in equation form as:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
Hence, 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.