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Others [13] [failed verification] define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition [14]), making the parallelogram a special type of trapezoid. The latter definition is consistent with its uses in higher mathematics such as calculus. This article uses the inclusive definition and considers ...
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
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.
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 ...
An object is therefore congruent to its mirror image (even if it is not symmetric), but not to a scaled version. Two congruent objects always have either the same shape or mirror image shapes, and have the same size. Objects that have the same shape or mirror image shapes are called geometrically similar, whether or not they have the same size ...
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. So, either a parallelogram doesn't have a midsegment (this, I think, is not the correct solution) or the definition of a trapezoid needs to be more restrictive to not include ...
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]
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 ...