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triangle




labeled triangle
A triangle is a three-sided polygon. The sum of the interior angles of a triangle is always 180, unless the triangle is drawn in a non-Euclidean geometry . Triangles can be classified either by their angles, as acute, obtuse, or right; or by their sides, as scalene (all different), isosceles (two the same), or equilateral (all equal). A right (or right-angled) triangle has one interior angle equal to 90°, and may be either scalene or isosceles (see Pythagoras' theorem).

Various formulae link the dimensions of a triangle (see diagram). The cosine formula states that a 2 = b 2 + c 2 - 2bc cos A, and the sine formula that a / sin A = b / sin B = c / sin C. If s = 1/2 (a + b + c), the area of the triangle is √[s(s - a)(s - b)(s - c)].


Other types of triangle

A Pythagorean triangle is a right triangle whose sides are integers. A primitive Pythagorean triangle is one whose sides are relatively prime.

A medial triangle is a triangle whose vertices are the midpoints of the sides of a given triangle. An orthic triangle is a triangle whose vertices are the feet of the altitudes of a given triangle.

A limping triangle is right triangle whose two shorter sides (i.e., those other than the hypotenuse) differ in length by one unit. An example is the 20-21-29 triangle (202 + 212 = 292).

The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC.


Related category

   • POLYGONS