TRIANGLE

(Lat. trlangulum.) A three-sided figure, which consequently has also three angles. Triangles are rectilineal, spherical, or curvilineal. Rectilineal or plane triangles are bounded by straight lines; spherical triangles are formed on the surface of a sphere by the intersection of the planes of three great circles; curvilineal triangles are those which are bounded by three curves of any kind whatever. Triangles receive other distinctive denominations from the relation of their sides and angles. Plane triangles are denominated equilateral when their three sides are all equal; isosceles when two only are equal; and scaleiM when all three are unequal. They are called right angled when one of the angles is a right angle; oblique angled when one of the angles is more than a right angle; and acute-angled when each of the angles is le than a right angle; and triangles are said to be similar when their angles are respectively equal each to each. The following are some of the principal properties of plane triangles. 1. The greater side is opposite the greater angle, and vice vers a. 2. The sum of any two sides is greater, and the difference of any two le than the third side. 3. The sum of the three angles is equal to two right angles; and if one of the sides be produced, the exterior angle is equal to both the interior and opposite ones. [s. 1269]