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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.
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 area of the parallelogram is the area of the blue region, which is the interior of the parallelogram. The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the ...
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]
The formulas and properties given below are valid in the convex case. The word cyclic is from the Ancient Greek κύκλος (kuklos), which means "circle" or "wheel". All triangles have a circumcircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be cyclic is a non-square rhombus.
For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: [2] A = bh (parallelogram).
SPOILERS BELOW—do not scroll any further if you don't want the answer revealed. The New York Times. Today's Wordle Answer for #1270 on Tuesday, December 10, 2024.
It remains true that some parallelograms (namely rectangles) are isosceles trapezoids (or trapeziums outside the USA), but a general parallelogram is not. The intersection of the two sets is the set of rectangles. D b f i r s 11:45, 12 August 2009 (UTC) What makes a trapezoid a trapezoid is not the line of symmetry.