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The base angles of an isosceles trapezoid are equal in measure (there are in fact two pairs of equal base angles, where one base angle is the supplementary angle of a base angle at the other base). Special cases
An isosceles trapezoid is a trapezoid where the base angles have the same measure. As a consequence the two legs are also of equal length and it has reflection symmetry . This is possible for acute trapezoids or right trapezoids (as rectangles).
For any isosceles trapezoid, tangent lines to the circumscribing circle at its four vertices form the four sides of a kite. This correspondence can also be seen as an example of polar reciprocation, a general method for corresponding points with lines and vice versa given a fixed circle. Although they do not touch the circle, the four vertices ...
[6] [7] The convex hull of an antiparallelogram is an isosceles trapezoid, and every antiparallelogram may be formed from an isosceles trapezoid (or its special cases, the rectangles and squares) by replacing two parallel sides by the two diagonals of the trapezoid. [4]
Trapezia (UK) and trapezoids (US) include parallelograms. Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.
Every isosceles tangential trapezoid is bicentric. An isosceles tangential trapezoid is a tangential trapezoid where the legs are equal. Since an isosceles trapezoid is cyclic, an isosceles tangential trapezoid is a bicentric quadrilateral. That is, it has both an incircle and a circumcircle. If the bases are a, b, then the inradius is given by [7]
Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles – a right kite.A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also ex-tangential.
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.