"Quad" in quadrilateral means four. Quadrilaterals are the type of polygons having four sides, four vertices. The interior angles of the quadrilateral on summation provide a value of 360°. For example, a quadrilateral ABCD has four sides AB, BC, CD and DA. The four angles ∠A, ∠B, ∠C, ∠D contained by these four sides always add up to 360°.
There are several types of quadrilaterals we will come across, Convex Quadrilaterals, Concave Quadrilaterals and Intersecting Quadrilaterals. Convex Quadrilaterals are the ones whose interior angles are always less than 180°. The diagonals of the figure join the opposite vertex, and in some cases, it bisects the angles at these vertices. Some examples of convex quadrilaterals are
The trapezium or Trapezoid is a quadrilateral having 4 sides, and two sides are parallel to each other. Isosceles Trapezoid is a trapezoid having 2 equal and opposite sides. Therefore, the angles contained by these sides, commonly known as the base angle, are also equal. A parallelogram is a quadrilateral whose opposite sides are parallel to each other. These sides are also equivalent, along with the opposite angles being equal. Rhombus is a type of parallelogram with all 4 sides of equal length. A rectangle is a quadrilateral with equal opposite sides and all angles measuring 90° A Square is a rectangle with all sides equal.
Concave Quadrilaterals have at least one angle more than 180°, and one of its diagonals lies outside the figure. Intersecting quadrilaterals are the ones having two non-adjacent intersecting sides.
This chapter further deals with the questions regarding all kinds of quadrilaterals that are important for exams. The chapter also includes several formulas to determine perimeter, area or other factors of the quadrilaterals.