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 Geometry is the part of maths that deals with
objects like points, lines, planes and space.
E.g. triangle, rectangle , circle etc.
 Points are exact locations in space and
are named using capital letters. They are
shown by small dots.
 To name a point
A point is designated by a capital letter which
is written next to the dot which represents it.
Thus points shown here will be referred to as
point A, point B ,point C .
 The representation of a line has only length and no
width or thickness .A line has no end points. A line
extends infinitely in both directions.
A few facts about line
There are an unlimited number of points on a line.
There are an unlimited number of lines through a
point.
Two lines can intersect in only one point
 A plane can be thought of as a flat surface . Our
desktop, the floor and classroom are models of planes.
A plane extends without limit in all directions. There
are three types-:
1.vertical 2.horizontal 3.parallel lines
Vertical and horizontal lines . e.g.. front wall of the classroom
Parallel lines . E.g.
 A ray has one end point and extends without
limit in one direction from the end point.
 E.g. a light torch gives rays of light, the sun
emanates the rays of light.
 A line segment is a portion of a line
with two fixed end points.
Fact
The shortest path connecting two
points is along the line segment.
 In geometry , any collection of points is called a
figure.
 If all the points in a figure are in one place ,
the figure is a plane figure.
 Closed figure-:A closed figure that
does not intersect itself.
 Open figures-:an opened figure that does
intersect itself.
 An angle is made up of two rays that
have the same end point. The end point
at which the two rays meet is called the
vertex of the angle. Each of the rays that
form the angle are called the arms of the
angle. The size of an angle depends on
the rotation up to the terminal side. The
amount of this rotation is called the
measure of the angle.
 An angle can be named in three ways-:
1. With three letters
2. With one letter
3. With numerals or a small letter
 Like any plane figure , an angle divides
the plane in which it lies into two parts.
One part is called the interior of angle
and other exterior of angle. Interior tells
about the inside of the figure and the
exterior , tells the outside of the figure.
A triangle is a simple closed figure made of three
line segments.
Parts of a triangle
A triangle six parts or six elements-:
1. Three sides : AB , BC , CA
2. Three angles : L BAC , L ABC , L CBA
A line segment joining a vertex to the mid-
point of the
side opposite to the vertex is called a
meridian of a
triangle.
ALTITUDES OF A TRIANGLES
An altitude of a triangle is the perpendicular
drawn from a vertex to the opposite side.
 The figure made up of four line segments is
called a quadrilateral . The points ABCD are
called its vertices.
 The four line segments AB , BC , CD & DA are
called its sides.
 The four angles L DAB ,L ABC ,L BCD , L CDA
are called its angles.
 The line segment joining two non-consecutive
vertices is called a diagonal . E.g. AB and BD
1.Two sides of a quadrilateral are said to be
adjacent sides .if they have a common end
point.
2.Two sides of a quadrilateral are said to be
opposite sides.
Adjacent angles and opposite angles
1.Two angles of a quadrilateral are said to be
adjacent angles
2.Two angles of a quadrilateral are said to be
One of the most important and familiar figure is
the circle .we come across hundreds of circles
in a day
A circle is a simple closed curve all of whose
points are at the same distance from a given
point O in the same plane .the given point O is
called the centre of the circle.
 Radius -:a line segment
joining the centre of
a circle to any point.
 Chord -: a line segment
joining any two parts
On a circle
 Diameter -: a chord that
passes through the
circle
Interior and exteriorof a circle
The interior of a circle contains all the points in the
plane whose distance from the centre is less than
the radius
The exterior of a circle contains all the points in the
 Secant -: a line which intersects the
circle at two distinct points
 Arc. -: a part (continuous) of a circle
 Semicircle -: a diameter divides a
circle into two equal parts
 Segment -: a chord of a circle that divides
the area enclosed by it into two parts
 Sector -: the part of the circle enclosed
by any two radii of the circle
 Concentric circle -: two or more circles
drawn with the same centre.
basic geometry

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basic geometry

  • 1.
  • 2.  Geometry is the part of maths that deals with objects like points, lines, planes and space. E.g. triangle, rectangle , circle etc.
  • 3.  Points are exact locations in space and are named using capital letters. They are shown by small dots.  To name a point A point is designated by a capital letter which is written next to the dot which represents it. Thus points shown here will be referred to as point A, point B ,point C .
  • 4.  The representation of a line has only length and no width or thickness .A line has no end points. A line extends infinitely in both directions. A few facts about line There are an unlimited number of points on a line. There are an unlimited number of lines through a point. Two lines can intersect in only one point
  • 5.  A plane can be thought of as a flat surface . Our desktop, the floor and classroom are models of planes. A plane extends without limit in all directions. There are three types-: 1.vertical 2.horizontal 3.parallel lines Vertical and horizontal lines . e.g.. front wall of the classroom Parallel lines . E.g.
  • 6.  A ray has one end point and extends without limit in one direction from the end point.  E.g. a light torch gives rays of light, the sun emanates the rays of light.
  • 7.  A line segment is a portion of a line with two fixed end points. Fact The shortest path connecting two points is along the line segment.
  • 8.  In geometry , any collection of points is called a figure.  If all the points in a figure are in one place , the figure is a plane figure.
  • 9.  Closed figure-:A closed figure that does not intersect itself.  Open figures-:an opened figure that does intersect itself.
  • 10.  An angle is made up of two rays that have the same end point. The end point at which the two rays meet is called the vertex of the angle. Each of the rays that form the angle are called the arms of the angle. The size of an angle depends on the rotation up to the terminal side. The amount of this rotation is called the measure of the angle.
  • 11.  An angle can be named in three ways-: 1. With three letters 2. With one letter 3. With numerals or a small letter
  • 12.  Like any plane figure , an angle divides the plane in which it lies into two parts. One part is called the interior of angle and other exterior of angle. Interior tells about the inside of the figure and the exterior , tells the outside of the figure.
  • 13. A triangle is a simple closed figure made of three line segments. Parts of a triangle A triangle six parts or six elements-: 1. Three sides : AB , BC , CA 2. Three angles : L BAC , L ABC , L CBA
  • 14. A line segment joining a vertex to the mid- point of the side opposite to the vertex is called a meridian of a triangle. ALTITUDES OF A TRIANGLES An altitude of a triangle is the perpendicular drawn from a vertex to the opposite side.
  • 15.  The figure made up of four line segments is called a quadrilateral . The points ABCD are called its vertices.
  • 16.  The four line segments AB , BC , CD & DA are called its sides.  The four angles L DAB ,L ABC ,L BCD , L CDA are called its angles.  The line segment joining two non-consecutive vertices is called a diagonal . E.g. AB and BD
  • 17. 1.Two sides of a quadrilateral are said to be adjacent sides .if they have a common end point. 2.Two sides of a quadrilateral are said to be opposite sides. Adjacent angles and opposite angles 1.Two angles of a quadrilateral are said to be adjacent angles 2.Two angles of a quadrilateral are said to be
  • 18. One of the most important and familiar figure is the circle .we come across hundreds of circles in a day A circle is a simple closed curve all of whose points are at the same distance from a given point O in the same plane .the given point O is called the centre of the circle.
  • 19.  Radius -:a line segment joining the centre of a circle to any point.  Chord -: a line segment joining any two parts On a circle  Diameter -: a chord that passes through the circle
  • 20. Interior and exteriorof a circle The interior of a circle contains all the points in the plane whose distance from the centre is less than the radius The exterior of a circle contains all the points in the
  • 21.  Secant -: a line which intersects the circle at two distinct points  Arc. -: a part (continuous) of a circle  Semicircle -: a diameter divides a circle into two equal parts
  • 22.  Segment -: a chord of a circle that divides the area enclosed by it into two parts  Sector -: the part of the circle enclosed by any two radii of the circle  Concentric circle -: two or more circles drawn with the same centre.