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An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base . An isosceles trapezoid is a trapezoid where the base angles have the same measure.
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
In a convex quadrilateral all interior angles are less than 180°, and the two diagonals both lie inside the quadrilateral. Irregular quadrilateral (British English) or trapezium (North American English): no sides are parallel. (In British English, this was once called a trapezoid. For more, see Trapezoid § Trapezium vs Trapezoid.)
A right tangential trapezoid. A right tangential trapezoid is a tangential trapezoid where two adjacent angles are right angles. If the bases have lengths a, b, then the inradius is [6] = +. Thus the diameter of the incircle is the harmonic mean of the bases. The right tangential trapezoid has the area [6]
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
A kite with three 108° angles and one 36° angle forms the convex hull of the lute of Pythagoras, a fractal made of nested pentagrams. [22] The four sides of this kite lie on four of the sides of a regular pentagon, with a golden triangle glued onto the fifth side. [16] Part of an aperiodic tiling with prototiles made from eight kites
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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.
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