6th Grade Geometry

1. Basic Terms
• The basic terms are point, line and plane.

2. Point
• A point depicts the position of an object. Its
just a location marker. It has no length,
breadth or height.
• A dot marked by a pencil, the corners of a
square , the tip of an ice cone are some
examples of a point. Points are named by
single capital letter.

3. LINE
• A line has length but it has no breadth. It is
absolutely straight and extends indefinitely in
both directions.
• Edge of a table ,sides of a rectangle are
examples of line.
• A line has no end points.

4. PLANE
• A Plane is never ending flat surface which
extends indefinitely in all directions.
• Every solid has a surface which may be flat or
curved. For example , the surface of a cuboid is
a flat surface where as the surface of a ball is a
curved surface.
• A plane has length and width but no thickness.

5. Naming a Plane
• A plane is commonly named by taking 3 or
more points on it which are not in the same
line.
• Since plane extends indefinitely , only portion
of plane is drawn and usually represented by
rectangle or a parallelogram.

6. Lines in a plane
If we draw two lines in a plane , if they intersect
at a point then that point is called the point of
intersection of two lines.
Lines that do not intersect at each other and they
have no point in common are called Parallel
lines.

9. Naming a Line
• A line is named by putting a single small letter
by its side or by naming two points in the line.
• The arrows on the end of the line indicates it
extends indefinitely on both directions.
• You can call the line below as

10. Line Segments
• We know a line is straight and extends
indefinitely on both directions.
• If we mark two points say A and B on a line ,
then the portion of the line between A and B
is a line segment.

11. Line Segments
• The distance between the points A and B is
the length of the line segment.
• We denote the line segment as
• The line segment has exactly two end points

12. Rays
• The part of the line that extends indefinitely in
one direction from a point, say ‘O’ on a line is
called ray.
• The point ‘O’ is the initial point or the
endpoint of the ray.

13. Naming the Rays
If there is a ray , and ‘O’ is the initial point and the
end is named as ‘A’ then we call the ray

14. Angles
• An angle is made up of two rays that meet at
common end point.
• The point is called the vertex of the angle.
• The rays are called the sides of the angle.

15. Naming the Angles

18. Rotation of Rays
• Rotation of rays makes an angle.
• The magnitude of angle is the amount of
rotation of rays rotated at its vertex.
• If the initial and final position of a rotating ray
are opposite to each other ,the angle formed
is a straight angle.

19. Rotation of rays
• If a rotating ray makes a complete revolution
and meets the initial ray , the angle formed is
a complete angle. One complete angle is 360
degree.

20. Rotation of Rays
• If the initial and final positions of ray coincides
without making any revolution , the angle
formed is zero angle.

21. Rotation of rays
• If the initial position of ray is horizontal and it
rotates to occupy vertical position OB , then
the angle formed is right angle.

22. Kinds of Angle
• An angle whose measure is greater than 90
degree and but less than 180 degree is called
an obtuse angle.

23. Kinds of Angle
• An angle whose measure is greater than 0
degree and less than 90 degree is called an
acute angle.

24. Kinds of Angle
• An angle whose measure is greater than 180
degree and less than 360 degree is called
reflex angle

32. Triangles

38. Angles in Triangle

40. Exterior Angles

41. Exterior Angle theorem
• The exterior angle of a triangle is equal to the
sum of the two interior opposite angles.

42. Calculate the angles

43. Calculate the angles

45. Quadrilaterals

49. Angles in Quadrilateral

50. Finding angles in a quadrilateral

51. Find the angles

52. Find the angles

53. A 2-dimensional enclosed figure made by joining 3 or more straight lines
is called a polygon. Polygons are also known as ‘flat figures’.
Polygon
Polygon Not a Polygon Not a
Polygon
(straight sides) (has a curve) (open, not
closed)

54. Polygon

58. Different regular polygons
The names of the regular polygons come from the number of sides they have.
Name Figure Sides Interior Angle
Equilateral triangle 3 equal sides Each angle is 60°
Square 4 equal sides Each angle is 90°
Pentagon 5 equal sides Each angle is 108°
Hexagon 6 equal sides Each angle is 120°
Heptagon 7 equal sides
Each angle is
128.57°
Octagon 8 equal sides Each angle is 135°

68. Cones and Cylinders
Cones and cylinders have curved surfaces as shown below.

69. Cones
If one end of a line is rotated about a second fixed line while keeping the line's
other end fixed, then a cone is formed. The point about which the line is rotated
is called the vertex and the base of the cone is a circle.
A cone is said to be right when the vertex is directly above the centre of the base.

70. The net of a three-dimensional object is a representation of its faces in two dimensions.
The net of a cone consists of the following two parts:
•a circle that gives the base;
and
•a sector that gives the curved surface

71. Cylinders
If a line is rotated about a second fixed line while keeping both lines parallel,
then a cylinder is formed.
•The base of the cylinder is a circle and the top of the cylinder is also a circle.
•A cylinder is said to be right when the line joining the centre of the base and
the centre of the top is perpendicular to the base of the cylinder.
•The cross-sections parallel to the base are circles and are all identical.

72. The net of a cylinder consists of three parts:
•One circle gives the base and another circle gives the top.
•A rectangle gives the curved surface.