Question

EXERCISE 5.1
Which of the following statements are true and which are false? Give reasons for your
answers.
(1) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A terminated line can be produced indefinitely on both the sides.
(iv) If two circles are equal, then their radii are equal.
(v) In Fig. 5.9, if AB =PQ and PQ = XY, then AB = XY.
Fig. 5.9​

Answer 1

Answer:

(1). false.

because, infinitely many straight lines can pass through a single point.

(2). false.

because, only one straight line can be drawn joining two distinct points.

(3). false.

because a terminated has two end point on both the sides, and can't be produced

indefinitely in both the directions.

( note - the meaning of terminate is to be ended).

(4).true.

when it is said that two circles are equal , then their circumference as well as area are equal.thus their radii are also equal.

(5). true.

if AB=PQ. ---------(1)

and PQ=XY--------(2)

multiplying eq----(1) and (2).

we get,

AB•PQ=PQ•XY

AB=XY.

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Answer 2

Question :-

1. Which of the following statements are true and which are false? Give reasons for your

(ii) There are an infinite number of lines which pass through two distinct points.

answers.

(1) Only one line can pass through a single point.

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

(iv) Iftwo circles are equal, then their radii are equal.

In Fig. 2.9. if AB=PQ and PQ=XY, then AB=XY.

​

Answer :-

(i) False

Reason : If we mark a point O on the surface of a paper. Using pencil and scale, we can draw infinite number of straight lines passing

through O.

(ii) False

Reason : In the following figure, there are many straight lines passing through P. There are many lines, passing through Q. But there is one and only one line which is passing through P as well as Q.

(iii) True

Reason: The postulate 2 says that “A terminated line can be produced indefinitely.”

(iv) True

Reason : Superimposing the region of one circle on the other, we find them coinciding. So, their centres and boundaries coincide.

Thus, their radii will coincide or equal.

(v) True

Reason : According to Euclid’s axiom, things which are equal to the same thing are equal to one another.

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