Question

question 3 of 10
which of the following states the pythagorean theorem?
a. in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
b. in a right triangle, the hypotenuse equals the sum of the squares of the legs.
c. in a right triangle, the hypotenuse equals the sum of the legs.
d. in a right triangle, the square of the hypotenuse equals the sum of the legs.

Explanation:

The Pythagorean theorem is a fundamental principle in geometry. It specifically pertains to right - angled triangles. The theorem states a relationship between the sides of a right - angled triangle. Let's analyze each option:

• Option A: This option correctly states that in a right triangle, the square of the hypotenuse (\(c^{2}\)) equals the sum of the squares of the legs (\(a^{2}+b^{2}\)), i.e., \(c^{2}=a^{2}+b^{2}\).
• Option B: The hypotenuse (\(c\)) is not equal to the sum of the squares of the legs (\(a^{2}+b^{2}\)). The correct relationship involves the square of the hypotenuse.
• Option C: The hypotenuse (\(c\)) is not equal to the sum of the legs (\(a + b\)). For example, if \(a=3\) and \(b = 4\), \(a + b=7\), but the hypotenuse \(c = 5\) (since \(3^{2}+4^{2}=5^{2}\)).
• Option D: The square of the hypotenuse (\(c^{2}\)) is not equal to the sum of the legs (\(a + b\)).

Answer:

A. In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.