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triangle (in mathematics)

triangle, in mathematics, plane figure bounded by three straight lines, the sides, which intersect at three points called the vertices. Any one of the sides may be considered the base of the triangle. The perpendicular distance from a base to the opposite vertex is called an altitude. The area of a triangle is equal to one half the product of the base and the corresponding altitude. The line segment joining the midpoint of a side to the opposite vertex is called a median. All three altitudes of a triangle go through a single point, and all three medians go through a single (usually different) point. In Euclidean geometry the sum of the angles of a triangle is equal to two right angles (180°). If all three angles of a triangle are equal, the triangle is called equilateral. An isosceles triangle has two equal angles. A scalene triangle is one in which all three angles are different. A right triangle has one right angle. In geometry it is shown that two triangles are congruent (i.e., are the same shape and size) if, in general, any three independent parts (sides or angles) of one are the same as the corresponding three parts of the other. The rules of congruency make it possible, in trigonometry, to compute the sides and the angles of a triangle when three of these values are known. The triangle is the simplest of the polygons (i.e., it has the least possible number of sides). Since any polygon can be broken up into triangles by drawing various diagonals, a complete theory of the measurement of triangles provides a complete theory of the measurement of all polygons. In non-Euclidean geometries, the angles of a triangle are either less than two right angles (hyperbolic geometry) or more than two right angles (elliptic geometry).

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triangle

tri·an·gle / ˈtrīˌanggəl/ • n. a plane figure with three straight sides and three angles: an equilateral triangle. ∎  a thing shaped like such a figure: a small triangle of grass. ∎  a situation involving three people or things, esp. an emotional relationship involving a couple and a third person with whom one of them is involved. ∎  a musical instrument consisting of a steel rod bent into a triangle and sounded by being struck with a small steel rod. ∎  a frame used to position the balls in pool and snooker. ∎  a drawing instrument in the form of a right triangle. ∎  (triangles) hist. a frame of three halberds joined at the top to which a soldier was bound for flogging.

triangles

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triangle

triangle three-sided figure. XIV. — (O)F. triangle or L. triangulum, sb. use of n. of triangulus three-cornered, f. TRI- + angulus ANGLE2.
So triangular XVI. — late L.; see -AR.

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triangle

triangle (try-ang-ŭl) n. (in anatomy) a three-sided structure or area; for example, the femoral triangle.

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Triangle

Triangle

a set of three.

Example : long wavering triangle of waterfowl, 1895.

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triangle

triangledraggle, gaggle, haggle, raggle-taggle, straggle, waggle •algal •angle, bangle, bespangle, dangle, entangle, fandangle, jangle, mangel, mangle, spangle, strangle, tangle, wangle, wide-angle, wrangle •triangle • quadrangle • rectangle •pentangle • right angle • gargle •bagel, finagle, Hegel, inveigle, Schlegel •beagle, eagle, illegal, legal, paralegal, regal, spread eagle, viceregal •porbeagle •giggle, higgle, jiggle, niggle, sniggle, squiggle, wiggle, wriggle •commingle, cringle, dingle, Fingal, intermingle, jingle, mingle, shingle, single, swingle, tingle •prodigal • madrigal • warrigal •surcingle • Christingle •boggle, goggle, joggle, synagogal, toggle, woggle •diphthongal, Mongol, pongal •hornswoggle •bogle, mogul, ogle •Bruegel •bugle, frugal, fugal, google •Dougal, Mughal •Portugal • conjugal •juggle, smuggle, snuggle, struggle •bungle, fungal, jungle •McGonagall • astragal •burghal, burgle, Fergal, gurgle

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