The straightforward elements of any kind of triangle are its sides and also angles. Triangles space classified relying on relative size of their elements.

You are watching: A triangle with all sides of equal length is a/an _______ triangle.

As regard your sides, triangles might be

Scalene (all sides room different)Isosceles (two sides room equal)Equilateral (all 3 sides space equal)

And as regard your angles, triangles may be

Acute (all angles are acute)Right (one angle is right)Obtuse (one angle is obtuse)Equiangular (all angles room equal)

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A triangle is scalene if every one of its 3 sides are various (in i m sorry case, the 3 angles are likewise different). If 2 of its sides room equal, a triangle is called isosceles. A triangle with all 3 equal political parties is dubbed equilateral. S. Schwartzman"s The words of Mathematics describe the etymology (the origins) the the words. The first two are of Greek (and related) origins; words "equilateral" is that Latin origin:

scalene (adjective): from the Indo-European source skel- "to cut." Greek skalenos originally meant "stirred up, hoed up." once a piece of ground is stirred up, the surface ar becomes "uneven," which was a later definition of skalenos. A scalene triangle is uneven in the sense that all three sides space of various lengths. The scalene muscles on each side the a person"s neck are called for your triangular appearance. A scalene cone or cylinder is one who axis is no perpendicular come its base; opposite facets make "uneven" angles through the base.isosceles (adjective): indigenous Greek isos "equal", that unknown former origin, and also skelos "leg". The Indo-European source (s)kel- "curved, bent" is found in scoliosis and also colon, obtained from Greek. In geometry, an isosceles triangle or trapezoid has two equal legs. It may seem strange the the root method "bent" also though the sides of a triangle or trapezoid space straight, but each leg is bent family member to the adjoining legs.

equilateral (adjective): native Latin æquus "even, level," and latus, stem later-, "side," both of uncertain origin. Related borrowings indigenous Latin space bilateral and multilateral. In geometry, it is intended triangle is one in which every sides room equal in length.

This is exactly how the two viewpoints are distinguished with Venn diagrams:

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As for the angles, a triangle is equiangular if all three of its angles are equal. Very early in the facets (I.5 and I.6) Euclid proved that in an isosceles triangle the basic angles space equal and, conversely, the political parties opposite same angles room equal. Native here, because that a triangle, the nature of being equilateral and equiangular room equivalent, and the latter is hardly ever mentioned. (For a polygon v the variety of sides better than 3 the equivalence no much longer holds.)

In Euclidean geometry, the amount of the angle in a triangle equates to 180°. It complies with that a triangle may have at many one obtuse or even right angle. (This additionally follows from the Exterior edge Theorem.) If among the angles in a triangle is obtuse, the triangle is called obtuse. A triangle through one appropriate angle is right. Otherwise, a triangle is acute; for every one of its angles room acute. (All the interpretations are naturally exclusive. Over there is no feasible ambiguity.)

The following diagram summarizes all possible triangle configurations. The varieties of triangles:

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I came throughout this diagram in who credits very first Steps in Geometry by G. A. Wentworth and G. A. Hill (Ginn, 1901).

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References

H. R. Jacobs, Geometry, 3rd edition, W. H. Freeman and Company, 2003S. Schwartzman, The words of Mathematics, MAA, 1994

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