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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. 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.
Position of some special triangles in an Euler diagram of types of triangles, using the definition that isosceles triangles have at least two equal sides, i.e. equilateral triangles are isosceles. A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas ...
An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. [1] Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered ...
The largest equilateral triangle inscribed in a Reuleaux triangle is the one connecting its three corners, and the smallest one is the one connecting the three midpoints of its sides. The subset of the Reuleaux triangle consisting of points belonging to three or more diameters is the interior of the larger of these two triangles; it has a ...
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]
A right-angled triangle where c 1 and c 2 are the catheti and h is the hypotenuse. In a right triangle, a cathetus (originally from the Greek word Κάθετος; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called a "side about the right angle".
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle. Triangles are congruent if they have all three sides equal (SSS), two sides and the angle between them equal (SAS), or two angles and a side equal (ASA) (Book I, propositions 4, 8, and 26).