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A quadrilateral is any four sided polygon. There is no requirement for it to have any parallel sides. However a trapezoid (American English called a Trapezium in British English) is a quadrilateral with one set of parallel sides. A parallelogram is a quadrilateral with two sets of parallel sides.
https://www.quora.com/How-many-parallel-sides-does-a-quadrilateral-have
An obtuse trapezoid with two pairs of parallel sides is a parallelogram. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). A Saccheri quadrilateral is similar to a trapezoid in the hyperbolic plane, with two adjacent right angles, while it is a rectangle in the Euclidean plane.
https://en.wikipedia.org/wiki/Trapezium_(shape)
A quadrilateral is a 2-dimensional closed shape with four straight sides. E.g. The shape ABCD shown here is a quadrilateral. A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, as is BD. There are seven types of quadrilaterals that can be divided into two groups: parallelograms and other quadrilaterals.
http://www.mathsteacher.com.au/year8/ch09_geometry/07_quad/quad.htm
OpenStudy is now Brainly! Get your free account and access expert answers to this and thousands of other questions. join brainly today. You can draw a quadrilateral with no parallel lines and at least one right angle.
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The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides (if they are not parallel; otherwise there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure, in contrast to the special cases below.
https://en.wikipedia.org/wiki/Trapezium_(shape)
Quad means four. The quad bike has 4 wheels, for example. So a Quadrilateral is a shape with 4 sides, this includes squares, rectangles, parallelogram and trapezium. All the above have at least 2 parallel sides. 4 sided shapes with no parallel sides are also quadrilateral’s also. It means a shape with 4 sides.
https://www.quora.com/How-many-parallel-sides-does-a-quadrilateral-have
Example 4.1 – Uses properties to identify, describe, classify, and distinguish among quadrilaterals: Quadrilateral is the “family” name given to closed four-sided shapes. A rectangle is a special type of quadrilateral because it has four right angles and two pairs of parallel sides. This quadrilateral has no right angles and no parallel sides. Part I: Use the grid on the next page.
http://www.narragansett.k12.ri.us/resources/necap%20support/gle_support/Math/resources_geometry/quad.htm
In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid (/ˈtræpəzɔɪd/) in American and Canadian English but as a trapezium (/trəˈpiːzɪəm/) in English outside North America.
https://en.wikipedia.org/wiki/Trapezium_(shape)
An equiangular quadrilateral, i.e. the one with all angles equal is a rectangle. All angles of a rectangle equal 90°. An equilateral quadrilateral, i.e. the one with all sides equal, is a rhombus. In a square, rectangle, or rhombus, the opposite side lines are parallel. A quadrilateral with the opposite side lines parallel is known as a parallelogram. If only one pair of opposite sides is required to be parallel, the shape is a trapezoid.
http://www.cut-the-knot.org/Curriculum/Geometry/Quadrilaterals.shtml
what is a quadrilateral with no parallel lines
 A quadrilateral with no parallel lines is a parallelogram is a quadrilateral with two sets of parallel sides.