Introduction to Euclid`s Geometry Test

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Introduction to Euclid`s Geometry Test - 1

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Question 1
1 / -0

Which of the following statements is true?

A
A point has only length.

B
A point has both length and breadth.

C
A point has only breadth.

D
A point has no dimensions.

Solution

As we know, a point has no length, no breadth and no height. So, a point has no dimensions.
Hence, (4) is the correct option.
Question 2
1 / -0

Which of the following statements is true?

A
Two distinct intersecting lines cannot be parallel to the same line.

B
A plane has no dimensions.

C
The edges of a surface are planes.

D
The ends of a line have only one dimension.

Solution

i) Two distinct intersecting lines cannot be parallel to the same line. This is correct.

ii) A plane has no dimensions.
This is false as a plane has two dimensions.

iii) The edges of a surface are planes.
This is false as a plane is a flat, two-dimensional surface that extends infinitely.

iv) The ends of a line have only one dimension.
This is false as the ends of a line have no dimensions.
Question 3
1 / -0

How many points are common between two distinct lines?

A
0 or 1

B
2 or 3

C
4 or 5

D
6 or 7

Solution

Two distinct lines can have no common point. If they are not intersecting, then they are parallel.
Two distinct lines can have one distinct point, if they are intersecting lines, i.e. two lines intersect at only one point.
Hence, the answer is '0 or 1'.
Question 4
1 / -0

When two planes intersect, we get _______.

A
a point

B
a line

C
another plane

D
None of these

Solution

When two planes intersect, we get a line.
Question 5
1 / -0

Find the minimum number of points that are required to draw a straight line.

A
1

B
2

C
3

D
4

Solution

Two points are required to draw a line.
Hence, (2) is the correct option.
Question 6
1 / -0

If B is a point on line AC, then which of the following is true?

A
AB = AC

B
BC = AC

C
AB + BC = 2AC

D
AB + BC = AC

Solution

We know that lines that coincide with each other are equal to one another.
Since AB + BC coincides with AC, AB + BC = AC.
Hence, (4) is the correct option.
Question 7
1 / -0

For every line l and for every point P (not lying on l), there does not exist a unique line passing through P

A
which is perpendicular to l

B
which is parallel to l

C
which is coincident with l

D
None of these

Solution

Line through P cannot be coincident to line l.
Hence, option (3) is the correct option.
Question 8
1 / -0

If a = b and c = d, which of the following relationships is true?

A
a – c = b + d

B
a – c = b – d

C
a + c = b – d

D
c – a = d + b

Solution

If a = b and c = d, then a – c = b – d [By Euclid's axiom, if equals are subtracted from equals, the remainders are equal.]
Question 9
1 / -0

Draw a line AB and mark a point P at some distance from it. How many lines can be drawn through 'P' that are parallel to AB?

A
Only one

B
Only two

C
Only three

D
Infinite

Solution

By Euclid's Playfair's axiom, for every line '' and for every point 'P', not lying on '', there exists a unique line 'm' passing through 'P' and parallel to ''.
Question 10
1 / -0

If a = d, b = c, e = f and m = n, which of the following relationships is true?

A
a + b = c + d

B
a + d = c + b

C
a + d = e + f

D
a – m = d + n

Solution

If a = d, b = c, e = f and m = n, then a + b = c + d. [By Euclid's axiom, if equals are added to equals, then wholes are equal.]
Question 11
1 / -0

There are two concentric circles. The radius of the outer circle is 12 cm. Which of the following measurements cannot be the radius of the inner circle?

A
13 cm

B
10 cm

C
11 cm

D
0.275 cm

Solution

As the radius of the outer circle (12 cm) is always greater than the inner circle, the inner concentric circle cannot have radius greater than 12 cm.
So, 13 cm cannot be the radius of the inner circle.
Question 12
1 / -0

In the given figure, AB = CD. Which of the following relationship is true?

A
AC = BC + CD

B
AB + BC = CD

C
AB – BC = BD

D
AC = CD – BD

Solution

AB = CD (given)

Adding BC to each side,
AB + BC = BC + CD
AC = BC + CD [AB + BC = AC]
Question 13
1 / -0

If a + b = 2c, b + c = 2d and c = d, then which of the following relationships is true?

A
a = d

B
a = 3d

C
a = c – d

D
a = 5c

Solution

Given:
a + b = 2c … (1)
b + c = 2d ... (2)
c = d … (3)
From (1) and (2),
a - c = 2c - 2d
a - d = 2d - 2d [c = d from (3)]
a - d = 0
a = d
Question 14
1 / -0

In the given figure, AB = CD. Which of the following relationships is true?

A
AC = BC + CD

B
AB + BC = CD

C
AC - BC = BD

D
None of these

Solution

AB = CD (given)
On adding BC both sides:
AB + BC = BC + CD
AC = BC + CD
Question 15
1 / -0

If a + b = 2c, b + c = 2d and c = d, which of the following relationships is true?

A
a = d

B
a = 3b

C
a = 2d

D
a = 2b

Solution

By Euclid`s Axiom,
If a + b = 2c, b + c = 2d and c = d,
a + b = 2c
Then
a + b = 2d (given c = d)
a + b = b + c (given b + c = 2d)
a = c
a = d