"Isosceles" redirects here. For other uses, see Isosceles (disambiguation).
Isosceles triangle
Isosceles triangle with vertical axis of symmetry
Type
triangle
Edges and vertices
3
Schläfli symbol
( ) ∨ { }
Symmetry group
Dih2, [ ], (*), order 2
Properties
convex, cyclic
Dual polygon
Self-dual
In geometry, an isosceles triangle (/aɪˈsɒsəliːz/) is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
and 25 Related for: Isosceles triangle information
mathematical study of isoscelestriangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isoscelestriangles have been used as decoration...
define an isoscelestriangle as one with at least two equal sides. The latter definition would make all equilateral trianglesisoscelestriangles. The 45–45–90...
legs, namely √2/4.: p.282 Triangles with these angles are the only possible right triangles that are also isoscelestriangles in Euclidean geometry. However...
the triangle inequality for distances in plane geometry using the construction in the figure. Beginning with triangle ABC, an isoscelestriangle is constructed...
geometry, the theorem that the angles opposite the equal sides of an isoscelestriangle are themselves equal is known as the pons asinorum (/ˈpɒnz ˌæsɪˈnɔːrəm/...
triangle formed by two diagonals and a side of a regular pentagon is called a golden triangle or sublime triangle. It is an acute isoscelestriangle with...
like the Weaver Stance. The Isosceles Stance is a simple stance, and is natural to perform under stress. Because the Isosceles Stance orients the torso of...
same triangle characterize it in terms of the three Pythagorean means of two numbers, or via the inradius of isoscelestriangles. This triangle is named...
right triangle is half of a rectangle which has been divided along its diagonal. When the rectangle is a square, its right-triangular half is isosceles, with...
an isoscelestriangle approaches 180°, and with the right inequality approaching equality only as the obtuse angle approaches 90°. If the triangle is...
not go through its incenter unless the triangle is isosceles.: p.231 For all non-isoscelestriangles, the distance d from the incenter to the Euler line...
of brotherhood and they allow a woman into their relationship, an isoscelestriangle is created" automatically, as "in Truffaut's film Jules et Jim". René...
with. The skinny triangle finds uses in surveying, astronomy, and shooting. The approximated solution to the skinny isoscelestriangle, referring to figure...
isoscelestriangle, from (Maxwell 1959, Chapter II, § 1), purports to show that every triangle is isosceles, meaning that two sides of the triangle are...
side (and follow the flag's diagonals). The "Y" embraces a black isoscelestriangle from which the arms are separated by narrow yellow or gold bands;...
also a right isoscelestriangle. It also follows that FC = n − (m − n) = 2n − m. Hence, there is an even smaller right isoscelestriangle, with hypotenuse...
designated in the picture). Now the triangle E 10 E 1 P {\displaystyle {E_{10}E_{1}P}\;} is an isoscelestriangle with vertex E 1 {\displaystyle E_{1}}...
disphenoid are isoscelestriangles, it is called a tetragonal disphenoid. In this case it has D2d dihedral symmetry. A sphenoid with scalene triangles as its...
isosceles right triangle". Retrieved 2011-05-01. Xu, Y. (1996). "On the minimum distance determined by n (≤ 7) points in an isoscele right triangle"...
which has never been dedicated for public purposes." The plaque is an isoscelestriangle, with a 25+1⁄2-inch (65 cm) base and 27+1⁄2-inch (70 cm) legs (sides)...
components of the associated triangle center are always equal. Therefore, all triangle centers of an isoscelestriangle must lie on its line of symmetry...
line only for isoscelestriangles, for which the Euler line coincides with the symmetry axis of the triangle and contains all triangle centers. The tangential...