what is the base of an isosceles triangle
the third side
title: Isosceles triangle text: two equal sides, and for isosceles sets, sets of points every three of which form an isosceles triangle. In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The angle included by the legs is called the "vertex angle" and the angles that have the base as one of their sides are called the "base angles". The vertex opposite the base is called the apex. In the equilateral triangle case, since all sides are equal, any side can be called the base. Whether an isosceles triangle title: Isosceles triangle text: 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 title: Isosceles triangle text: tetrakis hexahedron, pentakis dodecahedron, and triakis icosahedron, each have isosceles-triangle faces, as do infinitely many pyramids and bipyramids. For any isosceles triangle, the following six line segments coincide: Their common length is the height formula_1 of the triangle. If the triangle has equal sides of length formula_2 and base of length formula_3, the general triangle formulas for the lengths of these segments all simplify to This formula can also be derived from the Pythagorean theorem using the fact that the altitude bisects the base and partitions the isosceles triangle into two congruent right triangles. The Euler line of any triangle title: Isosceles triangle text: an equilateral triangle. The first solutions of the problem with unbounded oscillations were found in the isosceles three-body problem. Long before isosceles triangles were studied by the ancient Greek mathematicians, the practitioners of Ancient Egyptian mathematics and Babylonian mathematics knew how to calculate their area. Problems of this type are included in the Moscow Mathematical Papyrus and Rhind Mathematical Papyrus. The theorem that the base angles of an isosceles triangle are equal appears as Proposition I.5 in Euclid. This result has been called the "pons asinorum" (the bridge of asses) or the isosceles triangle theorem. Rival explanations for this name title: Isosceles triangle text: a special isosceles triangle with the property that the other two inscribed squares, with sides collinear with the sides of the triangle, are of the same size as the base square. A much older theorem, preserved in the works of Hero of Alexandria, states that, for an isosceles triangle with base formula_3 and height formula_1, the side length of the inscribed square on the base of the triangle is For any integer formula_35, any triangle can be partitioned into formula_36 isosceles triangles. In a right triangle, the median from the hypotenuse (that is, the line segment from the midpoint of