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A '''right angle''' is an angle that measures ninety degrees, or <math>\frac{\pi}{2}</math> radians - the same angle that is shown in the corner of a [[square]].  Another way to express this is that two [[line]]s 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[.]"<ref>''Elements'' Book I; available [http://www.gutenberg.org/etext/21076 here]</ref>

A '''right angle''' is an angle that measures ninety degrees, or <math>\frac{\pi}{2}</math> radians - the same angle that is shown in the corner of a [[square]].  Another way to express this is that two [[line]]s 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."<ref>''Elements'' Book I; available [http://www.gutenberg.org/etext/21076 here]</ref>

Right angles are very important in [[geometry]].  The most well known application is in [[Right triangle|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.

Right angles are very important in [[geometry]].  The most well known application is in [[Right triangle|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.