*Question 1:*

*What is the disadvantage in comparing line segments by mere observation?*

**Answer:**

When we compare two line segments of almost same lengths, we cannot be sure about the line segment of greater length. Therefore, it is not an appropriate method to compare line segments having a slight difference between their lengths. Therefore, this is the disadvantage in comparing line segments by mere observation.

*Question 2:*

*Why is it better to use a divider rule than a ruler, while measuring the length of a line segment?*

**Answer: **

While using a ruler, due to incorrect positioning of the eye positioning error may occur. Therefore, it is better to use divider rule than a ruler, while measuring the length of a line segment.

*Question 3: *

*Draw any line segment, say \(\overline{PQ}\). Take any point R lying in between P and Q. Measure the lengths of PQ, QR and PR. Is PQ = PR + RQ?*

*[Note: If P, Q, R are any three points on a line such that PR + RQ = PQ, then we can be sure that R lies between P and Q]*

**Answer:**

It is given that point R is lying somewhere in between P and Q. Therefore all these points are lying on the same line segment \(\overline{PQ}\) . Hence, for every situation in which point R is lying in between P and Q, it may be said that PQ =PR + RQ.

For an example,

\(\overline{PQ}\) is a line segment of 6 cm and R is a point between P and Q , such that it is 2 cm away from point Q. We can find that the measure of line segment \(\overline{PR}\) comes to 4 cm. Hence, relation PQ =PR + RQ is verified.

* *

*Question 4: *

*If P, Q and R: are three points on a line such that PQ = 5 cm, QR = 3 cm and PR = 8 cm, which one of them lies between the other two?*

**Answer:**

Given that,

PQ = 5 cm

QR = 3 cm

PR = 8 cm

Here, PR = PQ + QR

Therefore, point Q is lying between P and R.

*Question 5: *

*Verify, whether D is the midpoint of \(\bar{AG}\).*

**Answer: **

Given,

\(\bar{AD}\) = 4 – 1 = 3 units

\(\bar{DG}\) = 7 – 4 = 3 units

\(\bar{AG}\) = 7 – 1 = 6 units

∴ D is the mid point of \(\bar{AG}\).

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*Question 6:*

*If Q is the midpoint of \(\bar{PR}\) and R is the midpoint of \(\bar{QS}\), where P, Q, R, S lie on a straight line, say why PQ = RS ?*

**Answer: **

[Image]

Since Q is the midpoint of PR,

PQ = QR (1)

Since R is the midpoint of QS,

QR = RS (2)

From equation (1) and (2),

We may find that

PQ = RS