Regarding side length, a triangle is a right triangle if …
a² + b² = c²
A triangle is a right triangle if and only if it satisfies the Pythagorean Theorem, which states that the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (also known as the hypotenuse). Mathematically, this can be expressed as:
a^2 + b^2 = c^2
where a and b represent the lengths of the two shorter sides, and c represents the length of the hypotenuse. In a right triangle, one of the angles measures exactly 90 degrees, and that side opposite to the right angle is known as the hypotenuse. The other two sides are known as the legs of the right triangle.
Therefore, if a triangle satisfies the Pythagorean Theorem, it is a right triangle with the longest side being the hypotenuse.
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