Key Points - Understanding Quadrilaterals

- Parallelogram: A quadrilateral with each pair of opposite sides parallel. (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one another.
- Rhombus: A parallelogram with sides of equal length. (1) All the properties of a parallelogram. (2) Diagonals are perpendicular to each other.
- Rectangle: A parallelogram with a right angle. (1) All the properties of a parallelogram. (2) Each of the angles is a right angle. (3) Diagonals are equal.
- Square: A rectangle with sides of equal length. (1) All the properties of a parallelogram, rhombus and a rectangle.
- Kite: A quadrilateral with exactly two pairs of equal consecutive sides (1) The diagonals are perpendicular to one another (2) One of the diagonals bisects the other. (3) In the figure m∠B = m∠D but m∠A ≠ m∠C .
  
- Trapezium: A quadrilateral having exactly one pair of parallel sides.
- Diagonal: A simple closed curve made up of only line segments. A line segment connecting two non-consecutive vertices of a polygon is called diagonal.
- Convex: The measure of each angle is less than 180° .
Concave: The measure of at least one angle is more than 180°
Quadrilateral: Polygon having four sides.

Element of quadrilateral: 
(i) Sides: Line segments joining the points.  
(ii) Vertice: Point of intersection of two consecutive sides. 
(iii) Opposite sides: Two sides of a quadrilateral having no common end point. 
(iv) Opposite Angles: Two angles of a quadrilateral not having a common arm. 
(v) Diagonals: Line segment obtained by joining the opposite vertices. 
(vi) Adjacent Angles: Two angles of a quadrilateral having a common arm. 
(vii) Adjacent Sides: Two sides of a quadrilateral having a common end point.