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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 (see below). 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 scale or isoscles (see Pythagoras' theorem).

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.

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