Understanding Quadrilaterals

A polygon is a simple closed curve made up of only line segments.\n\nClassification of Polygons:\n\n1. Based on Number of Sides/Vertices:\n * 3 sides: Triangle\n * 4 sides: Quadrilateral\n * 5 sides: Pentagon\n * 6 sides: Hexagon\n * 7 sides: Heptagon\n * 8 sides: Octagon\n * n sides: n-gon\n\n2. Based on Convexity:\n * Convex Polygon: A polygon in which all interior angles are less than 180°. Any line segment joining any two points in the interior of the polygon lies completely in the interior of the polygon.\n * Concave Polygon: A polygon in which at least one interior angle is greater than 180°. A part of the line segment joining two points in the interior of the polygon may lie outside the polygon.\n\n3. Based on Regularity:\n * Regular Polygon: A polygon that is both equiangular (all angles are equal) and equilateral (all sides are equal).\n * Irregular Polygon: A polygon that is not regular, i.e., its sides are not all equal or its angles are not all equal (or both).

The sum of the interior angles of a polygon depends on the number of its sides. An n-sided polygon can be divided into (n-2) triangles by drawing diagonals from one vertex. Since the sum of angles in a triangle is 180°, the sum of interior angles of an n-sided polygon is (n-2) multiplied by 180°.

A quadrilateral is a polygon with four sides. The sum of the interior angles of any quadrilateral is (4-2) × 180° = 2 × 180° = 360°.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

1. Opposite sides are equal in length. (e.g., in parallelogram ABCD, AB = DC and AD = BC)\n2. Opposite angles are equal in measure. (e.g., in parallelogram ABCD, ∠A = ∠C and ∠B = ∠D)\n3. Adjacent angles are supplementary (their sum is 180°). (e.g., ∠A + ∠B = 180°, ∠B + ∠C = 180°, etc.)\n4. The diagonals bisect each other. (e.g., if diagonals AC and BD intersect at O, then AO = OC and BO = OD)