Page 102 - classs 6 a_Neat

LINE RESULT 3. Two lines in a plane either intersect at exactly one point or are parallel.

LINE A line segment extended endlessly on both sides is called a line. CONCURRENT LINES Three or more lines in a plane are said to be concurrent if all of them pass through the
Thus, a line segment AB extended on both sides and marked by arrows at the two ends, same point and this point is called the point of concurrence of the given lines.

represents a line, denoted by AB or BA.

A (Line AB) B
These arrows indicate that the line is endless in both directions. Sometimes, we represent a line
by a small letter l, m, n, etc.
In the adjoining figure, L is a line.
L
Two intersecting planes intersect in a line. In the above figure, the lines l, m, n, pare concurrent lines, since all these lines pass through the same point 0.
A line has no end points.
COLLINEAR POINTS Three or more points in a plane are said to be collinear if they all lie on the same line
RESULT 1. An unlimited number of lines can be drawn passing through a given point, as and this line is called the line of collinearity for the given points.
shown below.
R S
Q
B C
A
P
In the figure (1) given above, the three points A, B, C are collinear, while in the figure (ii), the
points P, Q, R a n d Sare noncollinear.
DISTINCTION BETWEEN A LINE SEGMENT, A RAY AND A LINE
In the above figure, lines l, m, n, p and q all pass through a gtven point 0.
Line segment Ray Line

RESULT 2. If two dlfferent points A and B are given in a plane then exactly one line can be 1.A line segment has two end 1.A ray has only one end point. 1.A line has no end point.
drawn passing through these points. points. 2.A ray does not have a definite 2.A line does not have a definite
2.A line segment has a defmite length. length.
length. 3. We cannot draw a ray on a paper. 3.We cannot draw a line on a
A B
3.A line segment can be drawn on We can simply represent it by a paper.We can simply represent
INTERSECTING LINES if there is a point P common to two lines l and m, we say that the two lines intersect a paper. diagram. it by a diagram.
at the point P and this point P is called the point of intersection of the given lines. 4. 4. 4.
A B is a line A B represents A B represents

segment AB. a ray AB. a ray AB.

IDEA OF SIMPLE CLOSED FIGURES

Intersecting lines STRAIGHT LINE We know that by moving a pencil along the straight edge of a ruler, we get a straight line.
PARALLEL LINES if no point is common to two gtven lines, it would mean that the lines do not intersect.
Such lines are known as parallel lines.

The rails of a railway line, opposite edges of a ruler and the opposite
sides of a rectangle are examples of parallel lines.
It is clear that either one point is common to two gtven lines or no point p
is common to them.
So, we obtain the following result. q
Parllel lines