Pythagorean theorem relates which elements of a right triangle?

Pythagorean theorem relates which elements of a right triangle?

• A. The lengths of the three sides (a^2 + b^2 = c^2)
• B. The angles of the triangle
• C. The area and perimeter
• D. The heights

Answer: (A)

The Pythagorean theorem is about the relationship between a right triangle’s side lengths. If you call the two legs a and b and the hypotenuse c, then a^2 + b^2 = c^2. This shows how long the sides are, not the angles or other measures. For example, a 3-4-5 triangle satisfies 3^2 + 4^2 = 5^2 (9 + 16 = 25), so c = 5. The theorem lets you find a missing side when you know the other two and also helps verify a triangle is right-angled by checking whether the squares add up this way. Area, perimeter, and altitudes involve different formulas, so they aren’t described by this relationship.

The Pythagorean theorem is about the relationship between a right triangle’s side lengths. If you call the two legs a and b and the hypotenuse c, then a^2 + b^2 = c^2. This shows how long the sides are, not the angles or other measures. For example, a 3-4-5 triangle satisfies 3^2 + 4^2 = 5^2 (9 + 16 = 25), so c = 5. The theorem lets you find a missing side when you know the other two and also helps verify a triangle is right-angled by checking whether the squares add up this way. Area, perimeter, and altitudes involve different formulas, so they aren’t described by this relationship.