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  2. Zonogon - Wikipedia

    en.wikipedia.org/wiki/Zonogon

    For equilateral zonogons, a -sided one can be tiled by () rhombi.) In this tiling, there is a parallelogram for each pair of slopes of sides in the 2 n {\displaystyle 2n} -sided zonogon. At least three of the zonogon's vertices must be vertices of only one of the parallelograms in any such tiling. [ 5 ]

  3. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. 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 ...

  4. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    The sum of all the internal angles of a simple polygon is π(n−2) radians or 180(n–2) degrees, where n is the number of sides. The formula can be proved by using mathematical induction : starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on.

  5. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    A non-convex regular polygon is a regular star polygon. The most common example is the pentagram , which has the same vertices as a pentagon , but connects alternating vertices. For an n -sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as { n / m }.

  6. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) π radians, or (n − 2)180 degrees, (n − 2)2 right angles, or (n − 2) ⁠ 1 / 2 ⁠ turn. The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles ...

  7. Rectilinear polygon - Wikipedia

    en.wikipedia.org/wiki/Rectilinear_polygon

    A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates ...

  8. Arrangement of lines - Wikipedia

    en.wikipedia.org/wiki/Arrangement_of_lines

    They form the interiors of bounded convex polygons or unbounded convex regions. These are the connected components of the points that would remain after removing all points on lines. [1] The edges or panels of the arrangement are one-dimensional regions belonging to a single line. They are the open line segments and open infinite rays into ...

  9. Parallelogon - Wikipedia

    en.wikipedia.org/wiki/Parallelogon

    In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted). [ 1 ] [ 2 ] Parallelogons have an even number of sides and opposite sides that are equal in length.