Introduction to Euclid's Geometry Test

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Introduction to Euclid's Geometry Test - 4

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Question 1
1 / -0

A plane has ________.

A
two dimensions

B
three dimensions

C
one dimension

D
no dimensions

Solution

A plane has two dimensions, i.e. length and breadth.
Question 2
1 / -0

Which of the following statements is true?

A
A circle can be drawn only with a specific value of radius.

B
A circle can be drawn with any centre and any radius.

C
A circle cannot be drawn with very large value of radius.

D
A circle can be drawn with a specific centre only.

Solution

By Euclid's postulate 3, a circle can be drawn with any centre and any radius.
Question 3
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 4
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 5
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 6
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 7
1 / -0

Which of the following statements is true?

A
A straight line lies evenly with all the points on itself.

B
A straight line does not lie evenly with all the points on itself.

C
Only end points lie on the straight line.

D
There is no difference between a plane and a surface.

Solution

According to Euclid, "A straight line lies evenly with all points on itself".

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Introduction to Euclid's Geometry Test - 4

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Introduction to Euclid's Geometry Test - 4

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Question 1

two dimensions

three dimensions

one dimension

no dimensions

Solution

Question 2

A circle can be drawn only with a specific value of radius.

A circle can be drawn with any centre and any radius.

A circle cannot be drawn with very large value of radius.

A circle can be drawn with a specific centre only.

Solution

Question 3

a – c = b + d

a – c = b – d

a + c = b – d

c – a = d + b

Solution

Question 4

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 5

a = d

a = 3d

a = c – d

a = 5c

Solution

Question 6

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 7

A straight line lies evenly with all the points on itself.

A straight line does not lie evenly with all the points on itself.

Only end points lie on the straight line.

There is no difference between a plane and a surface.

Solution

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