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A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3] Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other. One pair of opposite ...
a hexahedron with three pairs of parallel faces, a polyhedron with six faces , each of which is a parallelogram, and; a prism of which the base is a parallelogram. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all special cases of parallelepiped.
A less obvious corollary is that parallelogons can only have either four or six sides; [1] Parallelogons have 180-degree rotational symmetry around the center. A four-sided parallelogon is called a parallelogram. The faces of a parallelohedron (the three dimensional analogue) are called parallelogons. [2]
In geometry, a trapezoid (/ ˈ t r æ p ə z ɔɪ d /) in North American English, or trapezium (/ t r ə ˈ p iː z i ə m /) in British English, [1] [2] is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not ...
Given a norm, one can evaluate both sides of the parallelogram law above. A remarkable fact is that if the parallelogram law holds, then the norm must arise in the usual way from some inner product. In particular, it holds for the p {\displaystyle p} -norm if and only if p = 2 , {\displaystyle p=2,} the so-called Euclidean norm or standard norm.
Penn State is a win away from the national title game. The No. 6 Nittany Lions jumped out to a 14-0 lead and held on for a 31-14 win over No. 3 Boise State in the Fiesta Bowl. PSU advances to the ...
What does the year hold in store, and will 2025 be the comeback year for live music? Way.com looks at what went wrong in 2024 and why it could go right in 2025. 2024 is apparently the year the ...
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