Exercise 5.1

Q1

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

Sol

Solution: Comparing line segments by observation is fast but only useful of the difference in length between the line segmentsline is quite large.

In cases where, the difference is relatively small: there is a high chance of human error.

Q2

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

Sol

Solution: When using a ruler, the process involves aligning the edge of the ruler with the endpoints of the line segment and reading off the .

This can introduce errors due to parallax (the apparent shift in the position of an object when viewed from different angles) and the difficulty of precisely aligning the rulerdivider.

A divider eliminates alignment errors because it directly spans the distance between the twothree points.

You set the divider's tips on the line segment's endpoints and then transfer this measurement to a ruler for reading the .

This method ensures that the exact distance is measured without any misalignment.

Q3

3. Draw any line segment, say AB. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?

[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]

Sol

Solution:

From the figure,

AB =

BC =

AC =

AB = AC + CB = + = .

Hence, when drawing a line segment with two endpoints and selecting a point lying on the segment between the endpoints, the total of the original segment will be the sum of the lengths of the twothree smaller segments formed by this intermediate point and the two endpointsmidpoints.

Q4

4. If A, B, C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?

Sol

Solution:

We have, AB = cm and BC = cm

Therefore, AB + BC = 5 + 3 = cm

But, AC = cm

Hence, BC lies between A and CB.

Q5

5. Verify, whether D is the mid point of AG.

Sol

Solution:

From the given figure,

We have: AG = cm – 1 cm = cm

AD = 4 cm – 1 cm = cm

DG = 7 cm – 4 cm = cm.

AD + DG = 3cm + 3cm = cm

Therefore, AG = AD + DG , where AD = DG = cm

Hence, D is the midpoint of AG.

Q6

6. If B is the mid point of AC and C is the mid point of BD, where A, B, C, D lie on a straight line, say why AB = CD ?

Sol

Solution:

Since B is the midpoint of AC, we have: AB =

Since C is the midpoint of BD, we have: BC =

Given that AB = BC and BC = CD, we can conclude: AB =

Q7

7. Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always less than the third side.

Sol

Solution: We have seven randomly drawn triangles, let's check the side lengths for each of them.

(a) + 5.2 = ><= 5.2

(b) + 15 = ><= 8

(c) + 10 = ><= 15

(d) 8 + = ><= 5

(e) 10 + 10210 = ><= 10 ( Take 2 = 1.414 )