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  2. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    The rhombus has a square as a special case, and is a special case of a kite and parallelogram. In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means

  3. Kite (geometry) - Wikipedia

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

    A quadrilateral is a kite if and only if any one of the following conditions is true: The four sides can be split into two pairs of adjacent equal-length sides. [7] One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects ...

  4. Corresponding sides and corresponding angles - Wikipedia

    en.wikipedia.org/wiki/Corresponding_sides_and...

    The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...

  5. Orthodiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Orthodiagonal_quadrilateral

    A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal quadrilaterals that are also equidiagonal quadrilaterals are called midsquare quadrilaterals. [2]

  6. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of simple axioms. Until the advent of non-Euclidean geometry, these axioms were considered to be obviously true in the physical world, so that all the theorems would be equally true. However, Euclid's reasoning from assumptions ...

  7. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8]

  8. Newton's theorem (quadrilateral) - Wikipedia

    en.wikipedia.org/wiki/Newton's_theorem...

    Newton's theorem can easily be derived from Anne's theorem considering that in tangential quadrilaterals the combined lengths of opposite sides are equal (Pitot theorem: a + c = b + d). According to Anne's theorem, showing that the combined areas of opposite triangles PAD and PBC and the combined areas of triangles PAB and PCD are equal is ...

  9. Shape - Wikipedia

    en.wikipedia.org/wiki/Shape

    Artzy proves these propositions about quadrilateral shapes: If = (), then the quadrilateral is a parallelogram. If a parallelogram has | arg p | = | arg q |, then it is a rhombus. When p = 1 + i and q = (1 + i)/2, then the quadrilateral is square.