Question

1. Which of the following statements are true and
which are false ? Give reasons for your answers :
(i) 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.
(u) In given fig., if AB = PQ and PQ = XY,
then AB XY.
B
А.
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Answer 1

Answer:

Step-by-step explanation:

(i) False. Multiple lines can pass through a single point on different angles.

(ii) False. Only one line can be drawn between the two lines. One point is starting and another one is ending. No more lines are possible.

(iii) True. A terminated line is closed one between the two points. But it can be extended on either side against the two points.

(iv) True. The basic unit of a circle is Radius. So, if radius of the circles are equal, all circles are same.

(v) AB = PQ (eqn.1)

PQ = XY (eqn.2)

Substitute the PQ value in eqn.1

so, AB = XY

Answer 2

ANSWER :

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

• False.

Reason :- Through a single point, an infinite number of lines can pass. Hence, the statement "Only one line can pass through a single point" is False.

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

• False.

Reason :- Only one line can be pass through two distinct points. Hence, the statement "There are an infinite number of lines which pass through two distinct points" is False.

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

• True.

Reason :- A terminated line can be produced on both the sides indefinitely. Hence, this statement is True.

(iv) If two circles are equal, then their radii are equal.

• True.

Reason :- When two circles are equal, then their centre as well as circumference will coincide and the radii of the two circles will be equal. Hence the statement is True.

(v) In given fig., if AB = PQ and PQ = XY,then AB = XY.

• True.

Reason :- According to Euclid’s first axiom, "things which are equal to the same thing are equal to one another." Here, it is given that, AB line is equal to PQ line (AB = PQ) and PQ line is equal to XY line (PQ = XY). So, AB line will be equal to XY line (AB = XY). Hence, the statement is True.