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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the ...

  3. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. [6]: p. 14 [7]: p. 169 For a self-crossing quadrilateral, the Varignon parallelogram can degenerate to four collinear points, forming a line segment traversed twice.

  4. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. [a] Three equivalent definitions of parallelepiped are. a hexahedron with three pairs of parallel faces, a polyhedron ...

  5. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Internal angle (degrees) 90° (for square and rectangle) In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".

  6. Ackermann steering geometry - Wikipedia

    en.wikipedia.org/wiki/Ackermann_steering_geometry

    Ackermann geometry. The Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii. It was invented by the German carriage builder Georg Lankensperger in Munich in 1816 ...

  7. Pappus's area theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_area_theorem

    dark grey area = light grey area. Pappus's area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. The theorem, which can also be thought of as a generalization of the Pythagorean theorem, is named after the Greek mathematician Pappus of Alexandria (4th century AD), who ...

  8. Cross product - Wikipedia

    en.wikipedia.org/wiki/Cross_product

    The right-hand side is the Gram determinant of a and b, the square of the area of the parallelogram defined by the vectors. This condition determines the magnitude of the cross product. Namely, since the dot product is defined, in terms of the angle θ between the two vectors, as:

  9. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite respective angles ...

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