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  2. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...

  3. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. 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 ...

  4. Newton's theorem (quadrilateral) - Wikipedia

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

    Furthermore, let E and F the midpoints of its diagonals AC and BD and P be the center of its incircle. Given such a configuration the point P is located on the Newton line, that is line EF connecting the midpoints of the diagonals. [1] A tangential quadrilateral with two pairs of parallel sides is a rhombus.

  5. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

  6. List of two-dimensional geometric shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_two-dimensional...

    Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides; Hendecagram - star polygon with 11 sides; Dodecagram - star polygon with 12 sides; Apeirogon - generalized polygon with countably infinite ...

  7. Equidiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Equidiagonal_quadrilateral

    An equidiagonal kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangle Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles π/3, 5π/12, 5π/6, and 5π/12.

  8. Golden rectangle - Wikipedia

    en.wikipedia.org/wiki/Golden_rectangle

    The parallelogram between the pair of upright grey triangles has perpendicular diagonals in ratio ⁠ ⁠, hence is a golden rhombus. If the triangle has legs of lengths 1 and 2 then each discrete spiral has length φ 2 = ∑ n = 0 ∞ φ − n . {\displaystyle \varphi ^{2}=\sum _{n=0}^{\infty }\varphi ^{-n}.}

  9. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    The triangle angle sum theorem states that the sum of the three angles of any triangle, in this case angles α, β, and γ, will always equal 180 degrees. The Pythagorean theorem states that the sum of the areas of the two squares on the legs ( a and b ) of a right triangle equals the area of the square on the hypotenuse ( c ).

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