Definition | Point, Ray, Line, Collinear Points, Plane, Parallel Lines
Point
A point is an exact location.
A fine dot
represents a point.
It is denoted by capital letter – A, B, P, Q, etc.
In the given figure, P is a point.
Line Segment
The
straight path between two points A and B is called the line segment AB
A line segment has a definite length.
Ray
A portion of a line which starts at a point and goes off in a particular direction to infinity is known as ray.
Ray has one end point A. A Ray has no definite length. We write a ray
Line
A line segment when extended indefinitely in both the
directions is called the line
.
A line has no end points. A line has no definite length. It is denoted by small letters l, m, n, etc.
Incidence Axioms on lines
- A line contains infinitely many points.
- Through a given point, infinitely many lines can be drawn.
- One and only one line can be drawn to
pass through two given points A and B.
Collinear Points
Three or more than
three points are said to be collinear, if there is a line which contains them
all.
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| Collinear Points |
In
the given figure A, B, C are collinear points, while P, Q, R are noncollinear.
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| Non collinear Points |
Intersecting lines
Two lines having a
common point are called intersecting lines.
In the given figure, the lines AB and CD
intersect at a point O.
Concurrent Lines
Three or more lines
intersecting at the same point are said to be concurrent.
In the given figure, lines l, m, n pass through the same point P and therefore,
they are concurrent.
Plane
A plane is a surface such that
every point of the line joining any two points on it, lies on it.
Examples: The surface of a smooth wall;
the surface of the top of the table; etc.
Parallel Lines
Two lines l and m in a
plane are said to be parallel, if they have no point in common and we represent l∥ m
The distance between two parallel lines
always remains the same.
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