Question

pythagorean theorem proofs quick check
which statement explains the pythagorean theorem? (1 point)
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 legs 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

Explanation:

The Pythagorean Theorem specifically applies to right - angled triangles. It states a relationship between the sides: the sum of the squares of the two legs (the non - hypotenuse sides) is equal to the square of the hypotenuse.

• The first option is incorrect because the sum of interior angles being \(180^{\circ}\) is a general property of triangles, not related to the Pythagorean Theorem. Also, it wrongly states that the sum of the legs is equal to the square of the hypotenuse.
• The second option is incorrect as it mentions the sum of the square of the longest leg (which is the hypotenuse in a right - triangle, but if we assume a non - right - triangle with a long leg, it still doesn't follow the Pythagorean formula \(a^{2}+b^{2}=c^{2}\) where \(c\) is the hypotenuse of a right - triangle).
• The fourth option is about equiangular (and equilateral) triangles, which is a property of a different type of triangle (not related to right - triangles and the Pythagorean Theorem).

Answer:

If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.