In this chapter, several important geometric terms are included, which hold extreme importance in the later grades. The topics that are introduced not only will help students to build a foundation in geometry but will also help them to grasp the higherlevel concepts in the later grades easily.
The term ‘Geometry’ is the English equivalent of the Greek word "geometron".
"Geo" means "Earth", and "metron" means "Measurement."
Therefore, geometry means the measurement of the earth.
In our daily life, we observe and use objects having different shapes:
The ruler, pencil, and pen are straight.
Balls, bangles, coins, and sun are round shaped.
We can draw a point with the tip of a sharp pencil, the tip of a compass, or the pointed end of a needle.
A point is usually represented by a small dot and is named by a single capital letter of the alphabet.
These points will be read as point A, point B and point C.
A line segment corresponds to the shortest distance between two points.
The edge of a ruler and the edge of a box are examples of line segments.
Example: Use the figure to name:
a) Five points
b) Aline
c) Five line segments
a) Five points are O, B, C, D and E.
b) A line:
c) Five line segments are , , , , ,
Example: Use the figure to name:
(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.
a) Line containing point E is
b) Line containing point A is
c) Line on which O lies
d) Two pairs of intersecting lines are and , and
Examples of the ray are: Beam of light from a lighthouse and sun rays.
Thus a line segment extended endlessly in the direction from A to B, is a ray denoted by
Curve can be defined as the continuous movement of points in any and every direction.
1. Simple Curve
If a curve does not cross itself, then it is called a simple curve.
The curves shown below are not simple curves because they cross themselves.
2. Open Curve
The curve which does not form a closed path is called an open curve.
In an open curve, we can find at least one point at which the curve begins or ends.
3. Closed Curve
The curve which forms a closed path is called a closed curve.
In a closed curve, we cannot find any point at which the curve begins or ends.
A polygon is a closed figure formed of three or more line segments.
Examples of polygons are triangle, quadrilateral, pentagon and hexagon.
Example: Classify the following curves as
(i) Open
(ii) Closed
Answer:
Example: Consider the given figure and answer the questions:
(a) Is it a curve?
(b) Is it closed?
(a) Yes, it is a curve because a curve is drawn without lifting the pencil from the paper and without using a ruler.
(b) Yes, it is closed because the curve forms a closed path.
Example: Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon.
(b) An open curve made up entirely of line segments.
(c) A polygon with two sides.
Answer:
a) A closed curve that is not a polygon. b) An open curve made up entirely of line segments. c) A polygon with two sides cannot be drawn as minimum three line segments are required to make a polygon.
An angle is made up of two rays starting from a common endpoint.
Here, angle is formed by the rays and .The name of the angle is ∠AOB or ∠BOA, keeping the vertex in the
middle.
The interior of the angle is bounded by the arms of an angle.
The exterior of the angle is the region that lies outside the angle.
Example: In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF
(a)Point in the interior of ∠DOE is A.
(b) Points in the exterior of ∠EOF is C, A and D.
(c) Points on ∠EOF is E, B, O and F.
Example: Draw rough diagrams of two angles such that they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.
(a) One point in common
∠AOB and ∠COD have only one point in common, i.e. O
(b) Two points in common
∠BOC and ∠COD have two points in common, i.e. O and C
(c) Three points in common
∠BOC and ∠COD have three points in common, i.e. O, E and C.
(d) Four points in common
∠BOC and ∠COD have four points in common, i.e. O, C, E and F.
A triangle is a threesided polygon. It is the polygon with the least number of sides. It is denoted by the symbol ∆.
We see many triangleshaped objects in our daily life.Example:
Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
Point A is not in the interior or exterior of ∆ ABC as it is a vertex (a point where two line segments meet).
A foursided polygon is a quadrilateral. It has 4 sides and 4 angles.
Example: Draw a rough sketch of a quadrilateral PQRS.
Draw its diagonals.
Name them.
Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
The two diagonals are PR and QS. Diagonal PR and diagonal QS meet at point T which is in the interior of the quadrilateral PQRS.
A circle is a simple closed curve which is not a polygon. We see many things that are round: a clock, a bangle, and a coin.
Here is a circle with center O. A, P, B, and M are points on the circle.
Example: From the figure, identify:
(a) The center of circle
(b) Three radii
(c) A diameter
(d) A chord
(e) Two points in the interior
(f) A point in the exterior
(g) A sector
(h) A segment
(a) O is the center of the circle.
(d) ED is a chord
(b) OA, OB and OC are the three radii
(c) AC is the diameter of the circle
(e) O and P are the two points in the interior.
(f) Q is the point in the exterior
(g) OAB (shaded portion) is a sector
(h) ED (shaded portion) is a segment
94 videos347 docs54 tests

1. What is the difference between a point and a line segment? 
2. How are intersecting lines different from parallel lines? 
3. What is the significance of a ray in geometry? 
4. Can a curve be considered a straight line? 
5. How many sides does a polygon have? 

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