Intersecting and Parallel Lines

CBSE Class 6 Math Intersecting and Parallel Lines- If two lines have one common point, they are called intersecting lines. Get NCERT based study material at EduSaksham.

Intersecting and Parallel Lines

 

If two lines have one common point, they are called intersecting
lines.

If there is a point P common to two lines {color{Blue} }iota1 and {color{Blue} }iota2 , then the two
lines intersect at the point P and this
point P is called the point of
intersection of the given lines.

Parallel Lines
Two lines are said to be parallel if they are in the same plane and
do not intersect each other.

Perpendicular Lines
Two lines are said to be perpendicular when they intersect at
90 degree (right angle).

Example: Use the figure to name:
a) Five points
b) A line
c) Four rays
d) Five line segments

a) Five points are O, B, C, D and E.
b) A line: {color{Blue} overline{DB}}
c) Four rays are {color{Blue} overrightarrow{OB}}{color{Blue} overrightarrow{OC}}{color{Blue} overrightarrow{OE}} and {color{Blue} overrightarrow{OD}}
d) Five line segments are
{color{Blue} overline{OB}}{color{Blue} overrightarrow{OC}}{color{Blue} overrightarrow{OD}}{color{Blue} overrightarrow{OE}}{color{Blue} overrightarrow{DE}}


Example: Use the figure to name:
a) Line containing point E.
b) Line passing through A.
c) Line on which O lies

d) Two pairs of intersecting lines.
a) Line containing point E is {color{Blue} overline{AE}}
b) Line containing point A is {color{Blue} overline{AE}}
c) Line on which O lies {color{Blue} overline{CO}}
d) Two pairs of intersecting lines are {color{Blue} overline{AD}} and
{color{Blue} overline{CO}} , {color{Blue} overline{AE}} and {color{Blue} overline{FE}}


Example: How many lines can pass through
a) One given point?
b) Two given points?

a) Infinite number of lines can pass through a given point.


b) Only one line can pass through two given points.

 

 

Example: Consider the following figure of line MN. Say whether
following statements are true or false in context of the given figure.
(a) Q, M, O, N, P are points on the line {color{DarkRed} }overleftarrow{M}overrightarrow{N}

(b) M, O, N are points on a line segment {color{DarkRed} overline{MN}}.
(c) M and N are end points of line segment
{color{DarkRed} overline{MN}}.
(d) O and N are end points of line segment {color{DarkRed} overline{OP}}.
(e) M is one of the end points of line segment {color{DarkRed} overline{QO}}.
(f) M is a point on ray {color{DarkRed} overrightarrow{OP}} .
(g) Ray
 {color{DarkRed} overrightarrow{OP}}​ is different from ray {color{DarkRed} overrightarrow{OQ}} .
(h) Ray
 {color{DarkRed} overrightarrow{OP}}​ is same as ray {color{DarkRed} overrightarrow{OM}} .
(i) Ray
{color{DarkRed} overrightarrow{OM}} is not opposite to ray  {color{DarkRed} overrightarrow{OP}}​ .
(j) O is not an initial point of
 {color{DarkRed} overrightarrow{OP}}​ .
(k) N is the initial point of {color{DarkRed} overrightarrow{NP}} and {color{DarkRed} overrightarrow{NM}} .

a) True, points Q, M, O, N, P are points on the line MN. A line
passing through two points when extends indefinitely can contain
infinite number of points.
b) True, M, O, N are points on the line segment
{color{Blue} overline{MN}}.
c) True, M and N are end points of line segment
{color{Blue} overline{MN}}.
d) False, end points of line segment {color{Blue} overline{OP}} are O and P.
e) False, end points of line segment {color{Blue} overline{QO}} are Q and O and not M.
f) False, point M is not on ray {color{Blue} overrightarrow{OP}} .
g) True, the end points of ray
{color{Blue} overrightarrow{OP}} are O and P whereas the
endpoints of ray {color{Blue} overrightarrow{OQ}} are O and Q in the opposite direction.
Therefore the two rays
{color{Blue} overrightarrow{OP}} and {color{Blue} overrightarrow{OQ}} are different.
h) False, the end points of ray
{color{Blue} overrightarrow{OP}} are O and P whereas the
endpoints of ray {color{Blue} overrightarrow{OM}} are O and M in the opposite direction.
Therefore the two rays
{color{Blue} overrightarrow{OP}} and {color{Blue} overrightarrow{OM}} are different.
i) False, ray {color{Blue} overrightarrow{OM}} is opposite to ray
{color{Blue} overrightarrow{OP}} .
j) False, O is the initial point of ray
{color{Blue} overrightarrow{OP}} .
k) True, N is the initial point of {color{Blue} overrightarrow{NP}} and {color{Blue} overrightarrow{NM}} .

 

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