Basic Geometrical Ideas-Revision Notes

CBSE Class 6 Mathematics
Revision Notes

Basic Geometrical Ideas

  • A point determines a location.  It is usually denoted by a capital letter.
  • A line segment corresponds to the shortest distance between two points. The line segment joining points A and B is denoted byAB and BA denote the same line segment.
  • A line is obtained when a line segment like AB¯  is extended on both sides indefinitely; it is denoted by AB¯ or sometimes by a single small letter like l.
  • Two distinct lines meeting at a point are called intersecting lines.
  • Two lines in a plane are said to be parallel if they do not meet.
  • A ray is a portion of line starting at a point and going in one direction endlessly.
  • Any drawing (straight or non-straight) done without lifting the pencil may be called a curve. In this sense, a line is also a curve.
  • A simple curve is one that does not cross itself.
  • A curve is said to be closed if its ends are joined; otherwise it is said to be open.
  • A polygon is a simple closed curve made up of line segments. Here,
    (i) The line segments are the sides of the polygon.
    (ii) Any two sides with a common end point are adjacent sides.
    (iii) The meeting point of a pair of sides is called a vertex.
    (iv) The end points of the same side are adjacent vertices.
    (v) The join of any two non-adjacent vertices is a diagonal.
  • An angle is made up of two rays starting from a common end point.
  • Two rays OA¯ and OB¯ make AOB(or also called  BOA).
  • An angle leads to three divisions of a region:
  • On the angle, the interior of the angle and the exterior of the angle.
  • A triangle is a three-sided polygon.
  • A quadrilateral is a four-sided polygon.  (It should be named cyclically).  In any quadrilateral ABCD, AB¯  & DC¯ and  AD¯  & BC¯   are pairs of opposite sides. A & C and B & D are pairs of opposite angles. A is adjacent to B & D; similar relations exist for other three angles.
  • A circle is the path of a point moving at the same distance from a fixed point.  The fixed point is the Centre, the fixed distance is the radius and the distance around the circle is the circumference.
  • A chord of a circle is a line segment joining any two points on the circle.
  • A diameter is a chord passing through the Centre of the circle.
  • A sector is the region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
  • A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.
  • The diameter of a circle divides it into two semi-circles.