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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.
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.
At any selected angle of a general triangle of sides a, b, c, inscribe an isosceles triangle such that the equal angles at its base θ are the same as the selected angle. Suppose the selected angle θ is opposite the side labeled c. Inscribing the isosceles triangle forms triangle CAD with angle θ opposite side b and with side r along c.
The unique 6-point isosceles set in the plane. The shaded regions show four of the 20 isosceles triangles formed by triples of these points. In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle.
In the latter double inequality, the first part holds with equality if and only if the triangle is isosceles with an apex angle of at least 60°, and the last part holds with equality if and only if the triangle is isosceles with an apex angle of at most 60°. Thus both are equalities if and only if the triangle is equilateral. [7]: Thm. 1
Duplicate the right triangle to form the isosceles triangle ACP. Construct the circle with center A and radius b, and its tangent h = BH through B. The tangent h forms a right angle with the radius b (Euclid's Elements: Book 3, Proposition 18; or see here), so the yellow triangle in Figure 8 is right. Apply the Pythagorean theorem to obtain
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]
By convention only the first of the three trilinear coordinates of a triangle center is quoted since the other two are obtained by cyclic permutation of a, b, c. This process is known as cyclicity. [4] [5] Every triangle center function corresponds to a unique triangle center. This correspondence is not bijective. Different functions may define ...