A right angle is an angle that measures ninety degrees, or radians - the same angle that is shown in the corner of a square. Another way to express this is that two lines that are perpendicular are at right angles to one another. Euclid defined a right angle as the angle formed when "one line stands on another and makes the adjacent angles at both sides of itself equal."
Right angles are very important in geometry. The most well known application is in right angled triangles, where one of the three angles is a right angle. The Pythagorean theorem states that "the sum of the squares on the two legs of a right angled triangle is equal to the square on the hypotenuse". The legs are the shorter sides, that are opposite the two non-right angles, and the hypotenuse is the long side, opposite the right angle.
It may seem trivial, but right angles are very important in the building trades, since people want to live in houses with vertical walls and level floors.
- Elements Book I; available here