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height/altitude: trapezoid/trapezium with opposing triangles , formed by the diagonals. Given a convex quadrilateral, the following properties are equivalent, and each implies that the quadrilateral is a trapezoid: It has two adjacent angles that are supplementary, that is, they add up to 180 degrees.
For example, direct proof can be used to prove that the sum of two even integers is always even: Consider two even integers x and y. Since they are even, they can be written as x = 2a and y = 2b, respectively, for some integers a and b. Then the sum is x + y = 2a + 2b = 2(a+b). Therefore x+y has 2 as a factor and, by definition, is even. Hence ...
Any non-self-crossing quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite. [5] However, if crossings are allowed, the set of symmetric quadrilaterals must be expanded to include also the crossed isosceles trapezoids, crossed quadrilaterals in which the crossed sides are of equal length and the other sides are parallel, and the antiparallelograms ...
The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A l (half linear dimensions yields quarter area), and the area of the parallelogram is A ...
Trapezium, plural trapezia, may refer to: Trapezium, in British and other forms of English, a trapezoid, a quadrilateral that has exactly one pair of parallel sides; Trapezium, in North American English, an irregular quadrilateral with no sides parallel; Trapezium (bone), a bone in the hand; Trapezium Cluster, a group of stars in the Orion Nebula
A kite is a quadrilateral with reflection symmetry across one of its diagonals. Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides. [1] [7] A kite can be constructed from the centers and crossing points of any two intersecting circles. [8]
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.
The previous example employed the contrapositive of a definition to prove a theorem. One can also prove a theorem by proving the contrapositive of the theorem's statement. To prove that if a positive integer N is a non-square number , its square root is irrational , we can equivalently prove its contrapositive, that if a positive integer N has ...