Question

Which statement explains the Pythagorean Theorem?

answers:

If a tringle is a right tringle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side

If all angles in a triangle are of equal measure, then the length of all slides will be equal

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

Answer 1

The correct statement that explains the Pythagorean Theorem is:

**"If a triangle is a right triangle, then the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side)."**

However, since this exact phrasing is not provided among your choices, it seems you may have typographical errors in the answer choices:

- **The first choice** is incorrect as stated because it mixes up the terms: the longest leg should not be mentioned in relation to the hypotenuse. The correct term for the longest side in a right triangle is "hypotenuse."

- **The second choice** describes an equilateral triangle, not applicable to the Pythagorean Theorem.

- **The third choice** incorrectly states the relationship between the legs and the hypotenuse.

To summarize, none of the provided statements correctly convey the Pythagorean Theorem's principle. The accurate statement should be:

In a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two sides.