The Pythagorean theorem applies to which type of geometric figure?

• A. Equilateral triangles
• B. Isosceles triangles
• C. Acute triangles
• D. Right triangles

Answer: (D)

The Pythagorean theorem is about right triangles, the ones with a 90-degree angle. In such a triangle, if you call the two legs a and b and the side opposite the right angle the hypotenuse c, then a^2 + b^2 = c^2. This specific relationship arises because the two legs meet perpendicularly, and it reflects how areas of squares built on the legs relate to the square built on the hypotenuse. If a triangle isn’t right, that clean equality doesn’t hold in general (equilateral or acute triangles don’t have a hypotenuse whose square equals the sum of the squares of the other two sides). For non-right triangles, a broader formula called the law of cosines is used instead. So the theorem clearly applies to right triangles.