Quadrilateral is a plane, closed, geometric figure with four sides. A quadrilateral has four sides - AB, BC, CD and DA, four angles - ∠A, ∠B, ∠C, ∠D, two diagonals - AC and BD, and four vertices - A, B, C and D.
1. Trapezium: When one pair of opposite sides of quadrilateral is parallel, then it is called a trapezium. If non-parallel sides of a trapezium are equal, then it is called an isosceles trapezium.
2. Kite: When two pairs of adjacent sides of a quadrilateral are equal, then it is called a kite.
3. Parallelogram: When both the pairs of opposite sides of a quadrilateral are parallel, then it is called a parallelogram.
The opposite sides are equal. The opposite angles are equal. The diagonals bisect each other and each of them divides the parallelogram into two triangles of equal area.
4. Rectangle: It is a special type of parallelogram when one of its angles is right angle.
Opposite sides are equal. Each angle is a right angle. Diagonals are equal and bisect each other.
5. Square: When all the four sides of a parallelogram are equal and one of its angles is 90°, then it is called a square.
All sides are equal. Each of the angles measures 90°. Diagonals are equal and bisect each other at right angles.
6. Rhombus: When all four sides of a parallelogram are equal, then it is called a rhombus.
All sides are equal. Opposite angles are equal. Diagonals of a rhombus are unequal and bisect each other at right angles.
In a triangle the line-segment joining the mid points of any two sides is parallel to the third side and is half of it. The line drawn through the mid point of one side of a triangle parallel to the another side, bisects the third side.
Parallelograms on the same base (or equal bases) and between the same parallels are equal in the area.
Triangles on the same base (or equal bases) and between the same parallels are equal in area.
Triangles on equal bases having equal areas have their corresponding altitudes equal.