# 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

## 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

## 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.

## 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.