Introduction
We are familiar with plane figures bounded by straight line segments as sides. They are known as Polygons. Polygon is a word of Greek origin. It means figure with many angles implying many sides.
Properties of Parallelogram
Parallelogram is a quadrilateral whose opposite sides are parallel and equal. A rectangle, a rhombus and a square are considered as parallelograms.
Area of a Parallelogram
The area of a polygon is the number of square units inside the polygon.
Area of a rectangle
The formula for the area of a rectanhle = A = Length x Breadth =l x b
Area of a Trapezoid
The area of a Trapezoid =(a+b)*h/2
Theorem1
The diagonals of a parallelogram bisect each other.
Quadrilateral to be a Parallelogram
If both pairs of opposite sides of a quadrilateral are equal, then this could become sufficient Conditions for a quadrilateral to be a parallelogram.
Theorem2
If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.
Theorem3
A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel.
Special Parallelograms
Rectangles, rhombuses and squares belong to the set of parallelograms.
Theorem4
Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other.
Converse of Theorem4
If two diagonals of a parallelogram are equal, it is a rectangle.
Theorem5
The diagonals of a rhombus are perpendicular to each other.
Converse of Theorem5
If the diagonals of a parallelogram are perpendicular then it is a rhombus.
Theorem6
The diagonals of a square are equal and perpendicular to each other.
Converse of Theorem6
If in a parallelogram, the diagonals are equal and perpendicular, then it is a square.
Theorem7
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
Converse of Theorem7
A straight line drawn through the mid-point of one side and parallel to another side of a triangle bisects the third side.
Theorem8
If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equal.
Summary
Quadrilateral : A plane closed figure formed by four line segments is called a quadrilateral.
