 # Fundamental Concepts of 2 Dimensional Geometric Shapes

You are familiar with geometric shapes such as point, line, angle, triangle, quadrilateral, circle and plane. In this article we will revise what you have learnt.

## Geometric Shapes – Point

A point is a basic geometrical shape/ object. It has some position but neither nay length nor any breadth.

To represent a point on paper, we make a dot using a sharp pencil. We denote points by capital letters, such as A, B, C, P and X.

### Collinear Points

If three or more points lie on a straight line, we say that these points are collinear. In the figure, A, B and C are collinear points, while A, E and F are non-collinear points

To learn more about the point in geometry you can read the post : Definition of Point in Geometry and 3 Types of Points

## Geometric Shapes – Line

A straight line (simply called a line) is formed by a collection of points. A line has some position, shape and length but neither any breadth nor any thickness.

It can be extended on either side to any length; so it has no end points. In figure, this is shown by arrowheads at either end of the line. A line is denoted by any two points on it; for example, line AB. It may also be denoted by a small letter (e.g. l, m, n, etc.).

### Ray

A ray is a part of a straight line. It extends indefinitely in one direction from a fixed point. In figure, this is represented by an arrowhead in one direction.

A ray has one end point – the fixed point from which it starts is called the initial point. It is denoted by the initial point and any other point on it, such as ray AB.

### Line Segment

The part of straight line between two given points is called a line segment. A line segment has two end points and finite length. The line segment between the points A and B is denoted as $\overline{AB}$

If C is a point on the line segment AB such that AC = CB = ½ AB then C is called the middle point (or midpoint) of AB.

### Properties of lines

The following properties of lines are to be universally true.

1. Property 1: There are an infinite number of points on a straight line.
2. Property 2: An infinite number of straight lines can be drawn through a given point.
3. Property 3: One and only one straight line passes through two different given points (or two distinct points determine a straight line).
4. Property 4: Two different straight lines cannot have more than one point in common.

### Concurrent Lines

If three or more straight lines have one point in common then these lines are called concurrent lines. In the figure, l, m and n are three concurrent lines and O is the point of concurrency.

## Geometric Shapes – Triangle

A triangle is a plane that is bounded by three straight lines. In the figure ABC is a triangle.

A triangle has a total of three parts. Three sidess, three angles and three vertices.

A plane bounded by four straight lines is called a quadrilateral. In the figure ABCD is a quadrilateral.

Every quadrilateral has four sides, four angles and two diagonals.

## Geometric Shapes – Circle

A circle is a shape consisting of all points in a plane that is a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the center is called the radius.

## Geometric Shapes – Plane

A plane is a flat surface that has some length and breadth but no thickness. The surface of a sheet of paper and a tabletop are examples of a plane. In fact, they are parts of planes, because a plane is supposed to extend infinitely. It is made up of an infinite number of lines and hence and infinite number of points.

### An important property of a plane

If two points on a line lie in a plane then every point on the line lies in the plane. This follows from the fact that two point are enough to determine a straight line.

 Quiz

## Check What You Have Just Revised

Their are some multiple choice question on fundamental concept of 2 dimensional geometric shapes, try to complete to check your progress… 0

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