Basic geometrical concepts
Let us take up ideas of some terms in geometry. This will help you to know more of geometry, particularly of figures with which some of you are familiar.
What is a Point?
Take a sharp pencil and make a dot on a plane sheet of paper or take a needle and prick on a paper will give you the physical examples to the idea of a point. Point is to be thought of as a location in space. It has no dimensions and so we cannot see a point or feel a point or move a point. A pencil dot marked by the most sharpened pencil does not in the strictest sense of the term represent a point. We can say it is a picture of a point.
A point is the basic unit of geometry. It shows an exact position.
Illustrations of points
A point is named by a single capital letter of the alphabet such as A, P, C, as shown below and read as ‘point A’, ‘point P’ and ‘point C’. The top of a cone, corners of square/tables are examples of points. Distant stars appear as points
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What is a Line?
Fold a piece of paper and press the two parts together. On unfolding it, you will see that a straight crease is formed. You just think of the trail from the jet plane, straight string of a kite while flying it, the edge of your desk and edge of a floor tile are examples of a line. We can only represent a line by drawing with a pen or pencil but it is not the real line.
The representation of a line has only length and no width or thickness.
Illustrations of a line
Our drawing of line shows only part of a line. Lines have no endings; they go on and on. Lines have no endings; they go on and on. A line is represented by a straight mark with two arrow heads at the extremes. It emphasizes the fact that the lines extends infinitely.
Definition:
| A line is a collection of points going endlessly in both directions along a straight path |
A line is named by single lower-case letter as shown below.
Important Points to remember
Line has no end points.
There are an unlimited number of points on a line.
There are unlimited number of lines through a point
Two lines can intersect in only one point
Exactly one line passes through two points
What is a Plane?
Flat surfaces are known as plane surfaces and the other surfaces are curved surfaces. Surface of a black board is a part of plane. Surface of a sheet of paper is a part of plane.
Experiment
Place a sheet of paper on the desk. Mark two points A and B on the paper and join them by a line. Every point on this straight line lies on the sheet or on the plane which the sheet is a part. Push the opposite edges of the sheet towards each other and try to join the points; If we join them along the surface of the sheet, we need a curved line. Make small holes at A and B, pass thread through the holes and pull the thread tout. The thread represents the straight line through A and B. See that except A and B, no part of the thread lies on the surface of the sheet. When the opposite edges pushed towards each other, the surface of the sheet is curved and not plane.
Marked two points on flat sheets Sheet of paper with ends pushed towards each other
All points of line lie on sheet All points of l, do not lie on sheet
| A plane is a flat surface that goes on endlessly in all directions. |
Two lines in a plane
Given two lines in a plane, there are only two possibilities;
They intersect
Definition:
| When two lines intersect at a point, then the lines are called intersecting lines |
Perpendicular Lines
Definition:
| When two lines intersect at right angle, then the lines are called perpendicular lines. |
- They do not intersect
Definition:
| The two lines in the same plane and do not intersect are called parallel lines. |
Parallel lines around us:
- Opposite sides of book,
- Opposite edges of desks.
Vertical line
The center line which the two pages meet is an example for vertical line.
Horizontal line
Line between the floor and a wall in your class room is a horizontal line.
Oblique line
The edge of a slide is the example for oblique line (slant line)
