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Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second condition, or because it has no line of symmetry. In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram), and the diagonals have equal ...
The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is a trapezoid with no sides of equal measure, [3] in contrast with the special cases below.
A quadrilateral that is not a parallelogram has one and only one pedal point, called the Simson point, with respect to which the feet on the quadrilateral are collinear. [6] The Simson point of a trapezoid is the point of intersection of the two nonparallel sides. [7]: p. 186 No convex polygon with at least 5 sides has a Simson line. [8]
Definition: A trapezoid is a quadrilateral that has only one pair of parallel sides. The non parallel sides of a trapezoid are called legs. Definition: A parallelogram is a quadrilateral that has both pair of opposite sides parallel. Definition: An isosceles trapezoid is a trapezoid, whose legs have the same length.
The currently used definition of a trapezoid (i.e. a shape with two parallel sides) allows for the inclusion of parallelogram, which is fine. However, the definition of a midsegment then states that the midsegment is to be drawn from the midpoints of the non-parallel sides, which a parallelogram does not have.
An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular. [ 3 ] A convex quadrilateral with diagonal lengths p {\displaystyle p} and q {\displaystyle q} and bimedian lengths m {\displaystyle m} and n {\displaystyle n} is equidiagonal if and only if [ 4 ] : Prop.1
An isosceles trapezoid can also fulfill the requirements. Opposing sides can be equal in length but only one facing side is parallel. I think you mean adjacent sides, and then your trapezium (trapezoid) turns into a kite. If you really meant opposite sides, then see the first characterisation in the article to see that you have a parallelogram ...
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.