Introduction to Euclid's Geometry Test

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Introduction to Euclid's Geometry Test - 2

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Question 1
1 / -0

Which of the following statements is true?

A
A terminated line can be produced finitely from both ends.

B
A terminated line can be produced indefinitely on both the sides.

C
A terminated line can be produced finitely from one end and infinitely from the other end.

D
A terminated line cannot be measured.

Solution

By Euclid's postulate 2, a terminated line can be produced indefinitely on both the sides.
Question 2
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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 3
1 / -0

Which of the following statements is false?

A
The part is greater than the whole.

B
Things which are double of the same things are equal to one another.

C
Things which are halves of the same things are equal to one another.

D
If equals are subtracted from equals, the remainders are equal.

Solution

The part is not greater than the whole.
Rather the whole is greater than the part. [By Euclid's axiom]
Question 4
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Euclid's fifth postulate gives an idea about

A
isosceles triangles

B
circles

C
parallel and intersecting lines

D
lines and points

Solution

Euclid's fifth postulate gives an idea about parallel and intersecting lines. According to the fifth postulate, 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.
Question 5
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 6
1 / -0

If a = 2b and b = 4c, then which of the following relationships is true?

A
a = 6c

B
6a = c

C
a = 8c

D
c = 8a

Solution

If a = 2b and b = 4c
⇒ a = 2b
⇒ a = 2(4c) [∵ b = 4c]
⇒ a = 8c
Question 7
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'.

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Introduction to Euclid's Geometry Test - 2

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Introduction to Euclid's Geometry Test - 2

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Question 1

A terminated line can be produced finitely from both ends.

A terminated line can be produced indefinitely on both the sides.

A terminated line can be produced finitely from one end and infinitely from the other end.

A terminated line cannot be measured.

Solution

Question 2

a + b = c + d

a + d = c + b

a + d = e + f

a – m = d + n

Solution

Question 3

The part is greater than the whole.

Things which are double of the same things are equal to one another.

Things which are halves of the same things are equal to one another.

If equals are subtracted from equals, the remainders are equal.

Solution

Question 4

isosceles triangles

circles

parallel and intersecting lines

lines and points

Solution

Question 5

13 cm

10 cm

11 cm

0.275 cm

Solution

Question 6

a = 6c

6a = c

a = 8c

c = 8a

Solution

Question 7

0 or 1

2 or 3

4 or 5

6 or 7

Solution

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