Classification

Classifications**
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[ [|edit] ] By relative lengths of sides
Triangles can be classified according to the relative lengths of their sides: ||
 * In an **equilateral triangle**, all sides have the same length. An equilateral triangle is also a [|regular polygon] with all angles measuring 60°.[|[1]]
 * In an **isosceles triangle**, two sides are equal in length. [|[2]] An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length.
 * In a **scalene triangle**, all sides and internal angles are different from one another.[|[3]]
 * [[image:file:///C:%5CDOCUME%7E1%5CFerrari%5CCONFIG%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image002.gif width="122" height="110" caption="Equilateral Triangle" link="http://en.wikipedia.org/wiki/File:Triangle.Equilateral.svg"]] || [[image:file:///C:%5CDOCUME%7E1%5CFerrari%5CCONFIG%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image004.gif width="74" height="114" caption="Isosceles triangle" link="http://en.wikipedia.org/wiki/File:Triangle.Isosceles.svg"]] || [[image:file:///C:%5CDOCUME%7E1%5CFerrari%5CCONFIG%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image006.gif width="245" height="110" caption="Scalene triangle" link="http://en.wikipedia.org/wiki/File:Triangle.Scalene.svg"]]
 * Equilateral || Isosceles || Scalene ||

[ [|edit] ] By internal angles
Triangles can also be classified according to their [|internal angles], measured here in [|degrees]. A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and therefore such triangle is equilateral.
 * A **right triangle** (or **right-angled triangle**, formerly called a **rectangled triangle**) has one of its interior angles measuring 90° (a [|right angle] ). The side opposite to the right angle is the [|hypotenuse] ; it is the longest side in the right triangle. The other two sides are the //legs// or **catheti** [|[4]] (singular: [|**cathetus**]) of the triangle. Right triangles obey the [|Pythagorean theorem] : the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: //a//2 + //b//2 = //c//2, where //a// and //b// are the lengths of the legs and //c// is the length of the hypotenuse. [|Special right triangles] are right triangles with additional properties that make calculations involving them easier.
 * Triangles that do not have an angle that measures 90° are called **oblique triangles**.
 * A triangle that has all interior angles measuring less than 90° is an **acute triangle** or **acute-angled triangle**.
 * A triangle that has one angle that measures more than 90° is an **obtuse triangle** or **obtuse-angled triangle**.