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In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length or two angles of equal measure. 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.
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
The slant height of a right square pyramid is defined as the height of one of its isosceles triangles. It can be obtained via the Pythagorean theorem : s = b 2 − l 2 4 , {\displaystyle s={\sqrt {b^{2}-{\frac {l^{2}}{4}}}},} where l {\displaystyle l} is the length of the triangle's base, also one of the square's edges, and b {\displaystyle b ...
Acute and obtuse triangles; Equilateral triangle; Euler's line; Heron's formula; Integer triangle. Heronian triangle; Isosceles triangle; List of triangle inequalities;
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
The equilateral triangle, with three 60° angles, is acute. The Morley triangle, formed from any triangle by the intersections of its adjacent angle trisectors, is equilateral and hence acute. The golden triangle is the isosceles triangle in which the ratio of the duplicated side to the base side equals the golden ratio. It is acute, with ...
Let A'BC be the equilateral triangle having base BC and vertex A' on the negative side of BC and let AB'C and ABC' be similarly constructed equilateral triangles based on the other two sides of triangle ABC. Then the lines AA', BB', CC' are concurrent and the point of concurrence is the 1st isogonal center. Its trilinear coordinates are
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