Math՚s: Lines and Angles: Important Basic Concepts and Pair of Lines (For CBSE, ICSE, IAS, NET, NRA 2022)

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Point, Line and Angle

  • Plane- A plane is flat surface (2 dimensional) that has no boundaries. Ex- the top of a table, the floor of a room etc.
  • Point- A point is a dot that shows a location on a plane. It has zero dimension i.e.. no length or breadth. Ex- A grain of sand
  • Line- A line is a straight line made by joining two points on a plane and that extends endlessly on both the sides. It is one dimensional i.e.. has length only and no breadth.
  • Line Segment- It is a part of a line. It has end points on both the sides. Ex- The edges of a book.
  • A line segment is also the shortest path between two points.
  • Polygon- A closed figure whose all sides are line segment. Ex- triangle, quadrilateral, pentagon etc.
  • Ray- A ray is a line that has a definite initial point but no final point. i.e.. it starts from a point and extends infinitely in one direction only. Ex- Sunray- the sun is an end point and the ray spreads indefinitely.
  • Angle- An Angle is a figure that consist of two rays starting from a common point. Ex- The adjacent edges of a book make an angle equal to
Point, Line and Angle

Some Important Relations between Lines and Points

  • We can draw an infinite number of lines through a point.
  • One and only one line can be drawn passing through two given points.
  • If a line can pass through three or more points, then these points are said to be collinear.
  • If a line cannot be drawn passing through all three points (or more points) , then they are said to be non-collinear
Relations between Lines and Points

Pair of Lines: Intersecting and Parallel

A pair of lines at a time can either be intersecting or parallel.

  • Two lines that can meet at a point are pair of intersecting lines. This is because the distance between them changes at different points
  • Two lines that can never meet at any point are pair of parallel lines. The distance between the parallel lines remain the same at all points.
Pair of Lines

Three or More Distinct Lines in a Plane

Three or more distinct lines in a plane may-

  • Intersect in more than one point.
  • Intersect in one point only. In such a case they are called concurrent lines.
  • They may be non-intersecting lines i.e.. parallel to each other.
Lines in a Plane

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