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A '''right angle''' is an angle that measures ninety degrees, or <math>\frac{\pi}{4}</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.
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 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.
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.
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.
==References==
<references />
[[Category:Geometry]]
[[Category:Geometry]]