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Standard XII
Mathematics
Coordinate Axes in Three Dimensional Space
Question

State the following statement is True or False
If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common.
  1. True
  2. False

A
True
B
False
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Solution
Verified by Toppr

suppose lines l1 and l2 intersect at two disticnt points say P and Q.Then l1 contains points P and Q.
Also, l2 contains points P and Q.
So two lines l1 and l2 pass through two distinct points P and Q.
But only one line can pass through two different points. (axiom 3)
Hence, two lines cannot have more than one point in common.
∴ Option A is correct.

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Similar Questions
Q1
State the following statement is True or False
If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common.
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Q2
State the following statement is True or False
Two distinct lines intersecting each other in a plane can have two points in common
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Q3
Two distinct lines in a plane cannot have more than one point in common.
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Q4
Which of the following statements are true?
(i) A line segment has no definite length.
(ii) A ray has no end-point.
(iii) A line has a definite length.
(iv) A line AB↔ is same as line BA↔.
(v) A ray →AB is same as ray →BA.
(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two distinct lines cannot have more than one point in common.
(ix) Two intersecting lines cannot be both parallel to the same line.
(x) Open half-line is the same thing as ray.
(xi) Two lines may intersect in two points.
(xii) Two lines are parallel only when they have no point in common.
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Q5

Fill in the blanks so as to make the following statements true :

(i) Two distinct points in a plane determine a _________ line.

(ii) Two distinct ______ in a plane cannot have more than one point in common.

(iii) Given a line and a point, not on the line, there is one and only______ line which passes through the given point and is ______ to the given line.

(iv) A line separtes a plane into ______ parts namely the ______ and the ______ itself.

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