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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    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 ...

  3. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    The triangles in both spaces have properties different from the triangles in Euclidean space. For example, as mentioned above, the internal angles of a triangle in Euclidean space always add up to 180°. However, the sum of the internal angles of a hyperbolic triangle is less than 180°, and for any spherical triangle, the sum is more than 180 ...

  4. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    The four smaller triangles formed by the diagonals and sides of a convex quadrilateral have the property that the product of the areas of two opposite triangles equals the product of the areas of the other two triangles. [53] The angle at the intersection of the diagonals satisfies ⁡ = +, where , are the diagonals of the quadrilateral.

  5. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.

  6. Transversal (geometry) - Wikipedia

    en.wikipedia.org/wiki/Transversal_(geometry)

    Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles. [5]: 307 [3]: Art. 88

  7. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law).

  8. Equilateral triangle - Wikipedia

    en.wikipedia.org/wiki/Equilateral_triangle

    An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.

  9. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    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 with six faces , each of which is a parallelogram, and; a prism of which the base is a parallelogram.