Which theorem is used to find the length of a side in a right triangle?

The Pythagorean theorem is the appropriate theorem to use when finding the length of a side in a right triangle. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is often expressed mathematically as ( a^2 + b^2 = c^2 ), where ( c ) represents the length of the hypotenuse, and ( a ) and ( b ) represent the lengths of the other two sides.

When you know the lengths of any two sides of a right triangle, you can use the Pythagorean theorem to calculate the length of the third side. This is particularly useful in various geometric problems, including those involving distance, navigation, and construction.

The other theorems mentioned serve different purposes: the congruence theorem relates to proving triangles congruent, the triangle inequality theorem deals with the sums of the lengths of sides in any triangle, and the angle bisector theorem pertains to the segments created by an angle bisector affecting the sides of the triangle. Each of these theorems has its own application, but the P