Basic Geometrical Ideas - Revision Notes

 CBSE Class 6 Mathematics

Revision Notes
CHAPTER – 4
Basic Geometrical Ideas

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• 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−→−$\overrightarrow{AB}$ and BA−→−$\overrightarrow{BA}$ denote the same line segment.
• A line is obtained when a line segment like AB¯¯¯¯¯¯¯¯$\overline{AB}$  is extended on both sides indefinitely; it is denoted by AB¯¯¯¯¯¯¯¯$\overline{AB}$ 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¯¯¯¯¯¯¯¯$\overline{OA}$ and OB¯¯¯¯¯¯¯¯$\overline{OB}$ make ∠AOB$\mathrm{\angle }AOB$(or also called  ∠BOA$\mathrm{\angle }BOA$).
• 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¯¯¯¯¯¯¯¯$\overline{AB}$  & DC¯¯¯¯¯¯¯¯$\overline{DC}$ and  AD¯¯¯¯¯¯¯¯$\overline{AD}$  & BC¯¯¯¯¯¯¯¯$\overline{BC}$   are pairs of opposite sides. ∠A$\mathrm{\angle }A$ & ∠C$\mathrm{\angle }C$ and ∠B$\mathrm{\angle }B$ & ∠D$\mathrm{\angle }D$ are pairs of opposite angles. ∠A$\mathrm{\angle }A$ is adjacent to ∠B$\mathrm{\angle }B$ & ∠D$\mathrm{\angle }D$; 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.