what makes a right triangle

A right triangle is defined as a triangle that has exactly one angle measuring 90 degrees, known as the right angle

. This right angle is the largest angle in the triangle, and the side opposite this angle is called the hypotenuse, which is always the longest side

. The two sides that form the right angle are called the legs (or catheti), and they meet perpendicularly

. The relationship between the lengths of these sides is described by the Pythagorean theorem: the square of the hypotenuse length equals the sum of the squares of the lengths of the two legs, mathematically expressed as a2+b2=c2a^2+b^2=c^2a2+b2=c2, where ccc is the hypotenuse

. Additional properties of a right triangle include:

• It cannot have any obtuse angles; the other two angles must be acute (less than 90 degrees)

• The area of a right triangle is half the product of the lengths of the legs, 12ab\frac{1}{2}ab21​ab, where aaa and bbb are the legs

• Every right triangle can be inscribed in a circle where the hypotenuse is the diameter of the circle (Thales' theorem)

In summary, what makes a right triangle is the presence of one 90-degree angle, with the sides satisfying the Pythagorean theorem and the hypotenuse opposite the right angle