Gemetry Concepts: Plane, Points and Lines

Geometry is made up of two Greek words; Geo and Metrien, Geo means 'earth' and Metrien meaning 'to measure'. It was originated to meet the requirement of measurement of land. But now it is studied under two heads namely plane geometry and solid geometry.

Plane geometry is associated with the shapes which can be drawn on a piece of paper like line, triangle, square etc., whereas

Plane: It is a flat surface having length and breadth only and does not have height. It's a two dimensional figure.

Point: The figure whose length, breadth and height cannot be measured. It is defined by its position.

Line: A line is made up of infinite number of points and it has only length and doesn't have width (or breadth). Three or more points are said to be collinear if there is a line which contains all of them.

There are three types of lines.

Line: The first one given in the following picture is a simple. A line does not have end points so it extends in both the direction infinitely.

Line Segment: Second is line segment or simply called segment. It has two end points as shown in the picture the end points are A and B.

Ray: It extends in one direction and have one single end point only and this end point is knows as initial point. In the given picture A is the initial point.
Three types of lines
1. A line contains infinitely many points.

2. Only one line can pass through any two particular points. 
3. Two lines can intersect maximum at one point and this point is called point of intersection and these lines are called as intersecting lines.
Intersecting Lines 
4. Two or more line are said to be parallel if they lie at the same distance to each other. The symbol of parallel is this | | for example if AB and BC are parallel lines then they can be written as AB| |BC.
Parallel Lines
5. Through a given point there pass an infinite number of lines and these lines are called concurrent lines.
6. When more than three points lie on a plane they are called as co-planar points else they are called non-coplanar points.

7. When more than three lines lie on a plane they are called as co-planar lines else they are called non-coplanar lines.

8. When two planes intersect each other they form a line.

9. Two different lines which are perpendicular to a common line, these two lines are parallel to each other.

10. When two or parallel lines are intercepted by some other intercepting lines then the ratio of corresponding intercepts are equal. And intercepting line is generally called as a transversal.

11. There are an infinite number of planes which can pass through a given single point.

No comments:

Post a Comment

Hello, This is Vikas (your mentor) and this is a quick tutorial as how to post your comment.

You can use your gmail account to post your comments and in case you do not have a gmail account. Then you have two options. You can either choose 'Name/URL' option or 'Anonymous' option from 'Comment as:' menu.

If you are using 'Name/URL' option:
Just fill your name in the 'Name' box and hit 'Continue'.

And after that just type in your comment in the box provided and hit 'Publish'.

If you are using 'Anonymous' option:
In this case you will need to type your name in the comment box and then type your comment and hit 'Publish' button.

Just remember comment moderation is ON that means your comments will be published after our approval. So that only useful comments and content is available on the website.

Thank you and good luck for your exams :)