# Ex.5.1 Q1 Introduction to Euclids Geometry Solution - NCERT Maths Class 9

## Question

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 figure 5.9 if

\(AB = PQ\) and \(PQ = XY,\)

then \( AB = XY.\)

Figure 5.9

## Text Solution

(i) ** Reasoning:**

We can draw infinite number of lines through a given point.

**Steps:**

** False**

**Related problems**:

- What are concurrent lines?
- How many chords can be drawn though center of the circle?

(ii) **Reasoning:**

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

**Steps:**

**False**

We can draw only one line passing through two points.

(iii) **Reasoning:**

According to Postulate 2 :A terminated line can be produced indefinitely.

**Steps:**

**True**

We know that a straight line can be produced on both sides.

(vi) **Reasoning:**

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

**Steps:**

**True**

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

(v) **Reasoning:**

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

**Steps:**

**True**

By transitivity law, we know that, if \(a = b\) and \(b = c\)* *then \(a = c.\)

Here since \(AB = PQ \)and \(PQ = XY\) then \(AB = XY\) according to this law.

Let us consider \(AB =5 \;\rm{cm}\), then \(PQ\) will be \(5 \;\rm{cm}.\)

But \(PQ = XY\) so \(XY\) will also be \(5 \;\rm{cm}\). \(AB = PQ = XY\) which also implies \(AB = XY.\)