Curve: A figure formed on a plane surface by joining a number of points without lifting a pencil is called a curve.
Open Curve: A curve which does not end at the same starting point or which does not cut itself is called an open curve.
Closed Curve: A curve which cut itself or which starts and ends at the same point is called a closed curve.
Simple Closed Curve: A closed curve called a simple closed curve which does not intersect itself.
Polygon: A polygon is a closed figure bounded by three or more line segments such that each line segment intersects exactly two other points (vertices) .
Quadrilateral: A simple closed figure bounded by four line segments is called a quadrilateral, it has four sides i.e., AB, BC, CD and AD and four vertices as A, B, C and D and the sum of all angles of a quadrilateral is 360°
Parallelogram: A quadrilateral in which opposite sides are parallel and equal is called parallelogram; written as || gm. and the diagonals of a parallelogram bisect each other.
Properties:
- Opposite sides are equal and parallel.
- Opposite angles are equal.
- Diagonals bisect each other.
Rectangle: A parallelogram each of whose angle is 90° and diagonals are equal, is called a rectangle.
Properties:
- Opposite sides are equal and parallel.
- Each angle is a right angle.
- Diagonals are equal.
- Diagonals bisect each other.
Square: A quadrilateral in which all sides and angles are equal, is called a square.
Properties:
- All the sides are equal and parallel.
- Each angle is a right angle.
- Diagonals are equal.
- Diagonals bisect each other at a right angle.
Rhombus: A parallelogram having all its sides equal, is called a rhombus.
Properties:
- All the side are equal.
- Opposite angles are equal.
- Diagonals bisect each other at a right angle.
Trapezium: A quadrilateral in which two opposite sides are parallel and the other two opposite sides are non-parallel, is called a trapezium.
If two non-parallel sides of a trapezium are equal, then it is called an isosceles trapezium.
The line segment joining the mid-points of non-parallel sides of a trapezium is called it’s median.
Kite: A quadrilateral in which two pairs of adjacent sides are equal, is called a kite.
Properties:
Diagonals bisect each other at the right angle.
In the figure, m ∠B = m ∠D, but m∠A ≠ m ∠C
Paper is a very common example of a plane surface. The curve obtained by joining a number of points consecutively without lifting the pencil from the paper is called a plane curve. A circle is a very common example of a plane curve.
A polygon is a simple closed curve formed of only line segments. A triangle is a very common example of a polygon.
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