Table of contents  
Introduction  
Understanding Symmetry  
Mirror Images  
What is Geometry?  
Point  
Line Segment  
Plane Shapes  
Idea of Space  
Solids 
Symmetrical Figures
Understanding mirror images helps us notice how things change when we look at them in a mirror!
Whenever we look near to us, we see different objects of different shapes and sizes. Also, different figures hold different similarities. However, the question is how to find out which figure is what.
Geometry is all about shapes and how they work. Geometry is a branch of mathematics that deals with the study of shapes, sizes, properties of space, and the relationships between points, lines, angles, surfaces, and solids.
A tiny dot ‘·’ represents a point. We name points by a capital letter such as A, B, C, D, ... which we write near the dot.
A point shows an exact location or position. It has no length, breadth or depth.
Edurev Tips: A line segment has a fixed length.
Observe the following figures:
In the first figure, line segments CD and AB are meeting at the point A. In the second figure, line segments CD and AB are meeting at the point P. In the third figure, line segments AB and BC are meeting at the point B.
We use line segments to build figures as given below:
A line is different from a line segment. A line does not have a beginning or an end. The picture of a line is drawn by putting arrowheads at both ends. The arrowheads at ends tell us that it goes on and on in both directions.
The figure given below shows the line AB. It is denoted as:
 A line segment is a part of a line.
 A line has no end points and it has no fixed length.
A ray is a part of a line which can be extended endlessly in one direction only.
Think of the rays of the Sun. Do they have a starting place and then go on and on in one direction?
Look at the following figures:
What is the end point of ray PQ?
Ans: P
Of ray QP?
Ans: Q
Why is not the same as
Ans: Their directions and endpoints are different.
To measure the length of a line segment, a ruler is used.
To Draw a Line Segment of Given Length
Method
Suppose, we have to draw a line segment of length 6 cm.
Step 1: Place the ruler on the plane paper and hold it as shown in the figure.
Step 2: Mark two points A and B against the marks 0 and 6 on the ruler.
Step 3: Pressing the ruler evenly, join these two points A and B with a pencil. The line segment AB thus drawn is the required line segment 6 cm long.
If instead of joining the points against the marks 0 and 6, you had joined them against the marks 1 and 7, or 2 and 8 or 5 and 11 etc., you would have still drawn a line segment 6 cm long.
Edurev Tips: We will indicate the fact that measures of AB and CD are equal by writing AB = CD and for the sake of simplicity read that AB is equal to CD.
As, you can draw them on a sheet of paper or a plane surface, they are called plane shapes or plane figures.
The figure given on the right is a rectangle. It has four corners (vertices) and four sides.
If you measure its sides, you will find that:
Opposite sides of a rectangle are equal.
In the rectangle ABCD, we have:
Vertices: A, B, C, D;
Sides: AB, BC, CD, DA;
Diagonals: AC and BD
The line segment joining the opposite vertices of the rectangle is called its diagonal.
As can be seen from the figure, a rectangle has two diagonals. If you measure them, you will observe that the diagonals of a rectangle are of equal length.
Thus, AC = BD.
The corner of a plane figure is called a vertex. The plural of ‘vertex’ is ‘vertices’.
A square is a closed figure. It has four sides and four vertices. If you measure its sides, you will find that:
All the sides of a square are equal.
In the square PQRS, we have:
Vertices: P, Q, R, S;
Sides: PQ, QR, RS, SP;
Diagonals: PR and SQ
A square also has two diagonals, which are of equal length
Thus, in a square PQRS, we haveand diagonal
The figure shown alongside is of a triangle. It has three vertices and three sides. In the triangle XYZ, we have:
Vertices: X, Y, Z;
Sides: XY, YZ, ZX
The sides of a triangle may or may not be equal.
A circle is a simple closed curve. It does not have any corner or side.
Look at the figure given alongside:
Will the bullock move along a circular path, if the rope is tight.
Ans: Yes
If several stones are placed along the path, will the distance from the stake to each of these points be the same?
Ans: Yes
A circle has a centre. A line segment from the centre to the circle is called radius.
Point O is the centre. OA is a radius.
Drawing a circle
Compasses are used to draw circles. The pictures given below show how to do it.
Can you draw a tennis ball, a match box, an icecream, a die, a drum, etc. on a plain sheet of paper?
Ans: No
At the most you can represent a football by a circle. Such bodies are called solids.
They are 3dimensional objects and not flat like plane figures. Solid shapes have length, width and depth.
A solid occupies a fixed amount of space.
Some common solid shapes are shown below:
A solid occupies space. The part of a solid which we usually see and touch is called the surface of the solid. Solids have different types of surfaces.
The notebook and the blackboard have plane surfaces. The ball and the globe have curved surfaces.
Some objects like an unsharpened pencil (cylinder) have both types of surfaces.
1. Cube
2. Cuboid
3. Cylinder
4. Cone
5. Sphere
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