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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.
v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.
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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

Solution:

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

False because, we can draw infinite number of lines through a given point as shown below.

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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

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

False. According to Axiom 5.1, Given any two distinct points, there is a unique line that passes through them.

We can draw only one line passing through two distinct points as shown below.

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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

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

True. According to Postulate 2, a terminated line can be produced indefinitely.

We know that a straight line can be produced on both sides as shown using the dotted lines shown below.

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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

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

True. According to Postulate 3, A circle can be drawn with any center and any radius.

We know that, circles are equal, which means the circles are congruent. (Circles coinciding with each other). This means that circumferences are equal and so the radii of two circles are also equal.

v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

True. Line segments whose corresponding lengths are equal are equal to one another.

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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

By transitivity law, we know that, if a = b and b = c then a = c.

Here since AB = PQ and PQ = XY therefore, AB = XY according to this law.

Let us consider AB = 5 cm, then PQ will be 5 cm.

But PQ = XY so, XY will also be 5 cm.

Thus, AB = PQ = XY which also implies AB = XY.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 5

Video Solution:

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. v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

NCERT Solutions Class 9 Maths Chapter 5 Exercise 5.1 Question 1

Summary:

The statements (I) only one line can pass through a single point, (ii) there are an infinite number of lines which pass through two distinct points are false, whereas the statements (iii) a terminated line can be produced indefinitely on both the sides, (iv) if two circles are equal, then their radii are equal, and (v) in fig. 5.9, if AB = PQ and PQ = XY, then AB = XY are true.

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