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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.
adventitious quadrangles problem. A quadrilateral such as BCEF is called an adventitious quadrangle when the angles between its diagonals and sides are all rational angles, angles that give rational numbers when measured in degrees or other units for which the whole circle is a rational number.
For example, the numbers I, II, III, V, and X are used, but IV and VI are not used, since a rotation of 180 degrees can make a 4 easily confused with a 6. For example, if two triangles are drawn, the first pair of congruent sides can be marked with a single hatch mark on each. The second pair of congruent sides can be marked with two hatch ...
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
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.
In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle. More precisely, each three points should determine at most two distances; this also allows degenerate isosceles triangles formed by three equally-spaced points on a line.
A geometric way of deriving the sine or cosine of 45° is by considering an isosceles right triangle with leg length 1. Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then the two equal angles are each 45°.
Now, triangles ABC and BCD are isosceles, thus (by Fact 3 above) each has two equal angles. Hypothesis: Given AD is a straight line, and AB, BC, and CD all have equal length, Conclusion: angle b = a / 3 . Proof: From Fact 1) above, + = °. Looking at triangle BCD, from Fact 2) + = °.