Question

Explain the Pythagorean theorem.
A.
The Pythagorean theorem states that if the square of one side of a triangle is less than the sum of the squares of the other two sides, then the triangle is a right triangle.
B.
The Pythagorean theorem states that if the square of one side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is a right triangle.
C.
The Pythagorean theorem states that if a triangle is a right triangle, then the sum of the squares of its legs is greater than the square of its hypotenuse.
D.
The Pythagorean theorem states that if a triangle is a right triangle, then the sum of the squares of its legs equals the square of its hypotenuse.

Answer 1

Correct answer: D.

Explanation: In a right triangle the two sides that meet at the right angle are called legs (a and b) and the side opposite the right angle is the hypotenuse (c). The Pythagorean theorem states
a^2 + b^2 = c^2.
Example: For a 3–4–5 triangle, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

Converse and related facts: If for a triangle with sides a, b, c (c the longest) a^2 + b^2 = c^2, the triangle is right. If a^2 + b^2 > c^2 the triangle is acute; if a^2 + b^2 < c^2 it is obtuse.