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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles. The sum of the squares of the sides equals the sum of the squares of the diagonals.

  3. Bisection - Wikipedia

    en.wikipedia.org/wiki/Bisection

    To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector.

  4. Square - Wikipedia

    en.wikipedia.org/wiki/Square

    All four internal angles of a square are equal (each being 360°/4 = 90°, a right angle). The central angle of a square is equal to 90° (360°/4). The external angle of a square is equal to 90°. The diagonals of a square are equal and bisect each other, meeting at 90°.

  5. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects the other into equal lengths. Every dart and kite is bisect-diagonal. When both diagonals bisect another, it's a parallelogram. Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle.

  6. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2. Copernicus – who used Ptolemy's theorem extensively in his trigonometrical work – refers to this result as a 'Porism' or self-evident ...

  7. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    Twice the length of the bimedian connecting the midpoints of two opposite sides equals the sum of the lengths of the other sides. [16]: p. 31 Additionally, the following properties are equivalent, and each implies that opposite sides a and b are parallel: The consecutive sides a, c, b, d and the diagonals p, q satisfy the equation [16]: Cor.11

  8. Isosceles trapezoid - Wikipedia

    en.wikipedia.org/wiki/Isosceles_trapezoid

    The diagonals of an isosceles trapezoid have the same length; that is, every isosceles trapezoid is an equidiagonal quadrilateral. Moreover, the diagonals divide each other in the same proportions. As pictured, the diagonals AC and BD have the same length (AC = BD) and divide each other into segments of the same length (AE = DE and BE = CE).

  9. 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 ...