Download Q1. Define the following terms: (i) Line segment (ii) collinear points

Q1.
Q2.
Define the following terms: (i) Line segment (ii) collinear points
Given two distinct points
, is there a line that can pass through
Q3.
Q4.
How many such lines are there? Draw the figure also.
What are concurrent lines?
Given two distinct lines
,is there a point that lies on both
Q5.
?
? How
many such points are there?
Give a symbolic representation of the following statement:
If a quantity is part of another quantity , then can be written as the sum of
and sum thirdquantity.
Q6.
If
are collinear points and
Q7.
If
Q8.
Q9.
Q10.
Q11.
State Euclid’s fifth postulate.
Restate Euclid’s fifth postulate in simple language.
What is Playfair’s axiom?
Prove that two lines which are parallel to the same line, are parallel to each other,
i.e ,if
and
, then
.
Q12.
If
are intersecting lines,
and
, then prove that
show that
.
also intersected.
are parallel to a line , then
prove that
are
collinear.
Q13.
Find the measure of an angle which is
more that its complement.
Q14.
Find the measure of an angle which is
less than its supplement.
Q15.
Write true or false for the given statements:
(i) A terminated line can be produced indefinitely on both the sides.
(ii) Any number of lines can be drawn through two given points.
(iii) If two circles are equal then their radii are equal.
(iv) Sum of two right angles is
.
Q16.
Q17.
What do you understand by a consistent system of axioms?
In the given figures,
falls on lines
such that the sum of the interior
angles
lines
Q18.
on the right side of
. On which side of
will the
intersect?
Complete the following:
(i) If the sum of two angles is
(ii) if the sum two angles is
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they are called ………. angles.
they are called …….. angles.
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Q19.
Q20.
Consider the statement ‘ There exists a pair of straight lines that are everywhere
equidistant from one another’. Is this statement a direct consequence of Euclid’s
fifth postulate?
If a straight line falls on two straight lines such that the sum of interior angles on
the other side of ? What can you say about two such lines?
Answers
A1.
(i) The straight path between two points
A2.
(ii) Three or more points are said to be collinear, if there is a line which contains all
of them.
Yes, only one line.
A3.
A4.
Three or more lines intersecting at the same point are said to be concurrent.
If we draw two lines
in the plane of a paper, then either they intersect or
A5.
they are parallel. If they intersect, there will be one and only one point that lies on
both of them. If they are parallel, there will be no point which lies on both of them.
A6.Hint:
to get
A7.
is called the line segment.
Hint:
. Substitute for
in the first statement,
.
are intersecting lines and
intersect and
intersect.
A8.
A9.
A10.
If a straight line falling on two straight lines makes the interior angles on the same
side of it taken together less than two right angles, then the two straight lines, if
produced indefinitely meet on that side on which the sum of angles is less than
two right angles.
Given any straight line and a point not on it, there exist one and only one straight
line which passes through that point and never intersects the first line, no matter
how far they are extended.
For every line and for every point not lying on , there exist a unique line
passing through
and parallel to .
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A11.
Hint: Let
out side
. Then
intersect in a unique point
there are two lines
the parallel lines axiom. Hence
A12.
Hint: If
these lines through
. Thus through a point
both parallel to . This is a contradiction to
.
are parallel to a line , then point
lies outside
and
are all parallel to . But, by parallel lines axiom, one and only
one line can be drawn parallel to a given line through a point outside it. Therefore,
points
lie on the same line (collinear points).
A13.
A14.
A15.
(i) True
(ii)False
(iii) True
(iv) True
A16. A system of axioms is consistent if it is impossible to deduce from these axioms a
statement that contradicts any axiom or previously proved statement.
A17. The lines
will eventually intersect on the right side of
. (Euclid’s fifth
postulate.)
A18. (i) Supplementary
(ii) complementary
A19. Yes, the statement is a direct consequence of Euclid’s fifth postulate as the
perpendicular distance between the lines is equal everywhere.
A20. By Euclid’s fifth postulate the sum of the interior angles on the other sides of
will
also be equal to two right angles. The two lines will be parallel.
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