I came across this diagram in who credits First Steps in Geometry by G. The following diagram summarizes all possible triangle configurations. (All the definitions are naturally exclusive. Otherwise, a triangle is acute for all of its angles are acute. A triangle with one right angle is right. (This also follows from the Exterior Angle Theorem.) If one of the angles in a triangle is obtuse, the triangle is called obtuse. It follows that a triangle may have at most one obtuse or even right angle. In Euclidean geometry, the sum of the angles in a triangle equals 180°. (For a polygon with the number of sides greater than 3 the equivalence no longer holds.) From here, for a triangle, the properties of being equilateral and equiangular are equivalent, and the latter is seldom mentioned. Very early in the Elements ( I.5 and I.6) Euclid showed that in an isosceles triangle the base angles are equal and, conversely, the sides opposite equal angles are equal. This is how the two approaches are distinguished with Venn diagrams:Īs regard the angles, a triangle is equiangular if all three of its angles are equal. In geometry, equilateral triangle is one in which all sides are equal in length. Related borrowings from Latin are bilateral and multilateral. It may seem strange that the root means "bent" even though the sides of a triangle or trapezoid are straight, but each leg is bent relative to the adjoining legs.Įquilateral (adjective): from Latin æquus "even, level," and latus, stem later-, "side," both of uncertain origin. In geometry, an isosceles triangle or trapezoid has two equal legs. The Indo-European root (s)kel- "curved, bent" is found in scoliosis and colon, borrowed from Greek. Isosceles (adjective): from Greek isos "equal", of unknown prior origin, and skelos "leg". A scalene cone or cylinder is one whose axis is not perpendicular to its base opposite elements make "uneven" angles with the base. The scalene muscles on each side of a person's neck are named for their triangular appearance. A scalene triangle is uneven in the sense that all three sides are of different lengths. Scalene (adjective): from the Indo-European root skel- "to cut." Greek skalenos originally meant "stirred up, hoed up." When a piece of ground is stirred up, the surface becomes "uneven," which was a later meaning of skalenos. The first two are of Greek (and related) origins the word "equilateral" is of Latin origin: Schwartzman's The Words of Mathematics explain the etymology (the origins) of the words. A triangle with all three equal sides is called equilateral. If two of its sides are equal, a triangle is called isosceles.
Triangle isosceles acute install#
If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.Ī triangle is scalene if all of its three sides are different (in which case, the three angles are also different). This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Equilateral (all three sides are equal)Īnd as regard their angles, triangles may be.Triangles are classified depending on relative sizes of their elements. The basic elements of any triangle are its sides and angles.
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