22 August 2014

Basic Geometrical Ideas

Basic Geometrical Ideas ( Summary )

Points, Lines and Curves

  • The point, the line segment, the line and the ray are the fundamental elements of geometry.
  • A point represents a location or a position, and is dimensionless. It can be denoted by single capital letter of the English alphabet.
  • Line segments are defined as the shortest distance between two points.
  • A line segment joining points L and M is denoted by
  • A distance between the two end points of a line segment is the length of the line segment.
  • A line is made up of an infinite number of points that extend indefinitely in both directions.
  • A line containing points L and M is denoted by
  • A plane is said to be a very thin flat surface that does not have any thickness and is limitless.
  • A minimum of three points are required to represent a plane.
  • Curves can be defined as figures that flow smoothly without a break.
  • Curves that do not intersect themselves are called simple curves.
  • The end points of open curves do not meet. While the endpoints of closed curve join to enclose an area.
  • For a closed curve, you can identify three regions – the interior of the curve, the boundary of the curve and the exterior of the curve.

Angles, Polygons and Circles

  • A curve that does not cross itself is called a simple curve.
  • Angle is made up of two rays starting from one common end.
  • Simple closed curves made up of only line segment are called polygons.
  • A circle is a simple closed curve formed by a point moving at the same distance from a fixed point.
  • Two rays join at a common point to form an angle.
  • A polygon made up of three line segments is called a triangle.
  • A polygon made up of four line segments is called a quadrilateral.
  • A triangle has three vertices, three sides and three angles.
  • A quadrilateral has four vertices, four sides and four angles.
  • Sides that have a common vertex are called adjacent sides.
  • A circle is formed by a point moving at the same distance from a fixed point.
  • A circle is also a simple closed curve; however, it does not have any sides or angles.
  • An air is a part of the circumference of a circle.
  • A chord is a line segment joining two points that lie on a circle.
  • The part of a circle that is enclosed by a chord and an arc is called a segment of the circle.
  • A chord passing through the centre of the circle is called its diameter.
  • A diameter is the longest chord of a circle.
  • A diameter of a circle divides the circle into two halves. Each half is called a semi-circle.
  • A line segments that joints the centre of the circle and a point on the circle is called the radius of the circle.
  • The radius of a circle is half of the diameter.
  • A part of the circle that is enclosed by two radii and an arc is called a sector.

With our free PDF notes you can get success in any competitive or entrance exams like CTET,  KVS, NET, CAT, MAT, CMAT, SSC, B.ED, IBPS Recruitment, IAS, CSAT, State Civil Services Exams, UPTET, PSTET, HTET & many more. It also provides NCERT solutions, CBSE, NTSE, Olympiad study material, Indian General Knowledge, English, Hindi, Mathematics, Current affairs, Science, S.ST, model test papers, important Questions and Answers asked in CBSE examinations.