Types of quadrilateral

ADJACENT SIDES:

Any two sides with a common end-point (vertex) are called the adjacent sides of the polygon.

ADJACENT VERTICES:

The end-points of the same side of a polygon are known as the adjacent vertices.

DIAGONALS:

The line segments obtained by joining vertices which are not adjacent are called the diagonals of the polygon.

Polygons are primarily classified by the number of sides.

CONVEX AND NON-CONVEX POLYGON:

Polygons may be characterized by their convexity or type of non-convexity:

CONVEX POLYGON:

A polygon is a convex polygon if the line segment joining any two points inside it lies completely inside the polygon.The boundary of the polygon does not cross itself. All convex polygons are simple polygons.

Any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. Equivalently, all its interior angles are less than 180°.

CONCAVE OR NON-CONVEX POLYGON:

A polygon which is simple and  not convex is called a concave polygon. A line may be found which meets its boundary more than twice. In other words, it contains at least one interior angle with a measure larger than 180°.

Here, are some convex polygon and some concave polygons:

Clearly, convex polygons have no portions of their diagonals in their exteriors which is not true in case of concave polygons.

If there are n-sides of a convex polygons and n> 3, then it has diagonals. A triangle has no diagonals.

Star-shaped Polygon: the whole interior is visible from a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.

Self-intersecting Polygon: the boundary of the polygon crosses itself.  The term complex is sometimes used in contrast to simple..

Star polygon: a polygon which self-intersects in a regular way.

SYMMETRY:

• Equiangular: all its corner angles are equal.
• Cyclic: all corners lie on a single circle.
• Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular.
• Equilateral: all edges are of the same length. (A polygon with 5 or more sides can be equilateral without being convex.)
• Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon is also equilateral.
• Tangential: all sides are tangent to an inscribed circle.
• Regular: A polygon is regular if it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon.

REGULAR POLYGON:

A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.

e.g. The following are examples of regular polygons:

e.g. The following are not examples of regular polygons:

A regular Polygon is both equiangular and equilateral.

IRREGULAR POLYGONS

A polygon is called an irregular polygon, if all the sides are not equal.

A rectangle has all angles equal each equal to 90º but its all sides need not be equal. In fact, its opposite sides are equal. So, a rectangle is not a regular polygon.

QUADRILATERAL:

A four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees.

e.g.

RECTANGLE:

A four-sided polygon having all right angles. The sum of the angles of a rectangle is 360 degrees.

e.g.

SQUARE:

A four-sided polygon having equal-length sides meeting at right angles. The sum of the angles of a square is 360 degrees.

e.g.

PARALLELOGRAM:

A four-sided polygon with two pairs of parallel sides. The sum of the angles of a parallelogram is 360 degrees.

e.g.

RHOMBUS:

A four-sided polygon having all four sides of equal length. The sum of the angles of a rhombus is 360 degrees.

e.g.

TRAPEZOID:

A four-sided polygon having exactly one pair of parallel sides. The two sides that are parallel are called the bases of the trapezoid. The sum of the angles of a trapezoid is 360 degrees.

e.g.