NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1

# NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1 are the part of NCERT Solutions for Class 6 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1.

## NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1 (Rationalised Contents)

### Ex 5.1 Class 6 Maths Question 1.

What is the disadvantage in comparing line segment by mere observation?

Solution:
The disadvantage of comparing the lengths of two line segments simply by mere observation may not be accurate. So, we use divider to compare the lengths of the given line segments.

### Ex 5.1 Class 6 Maths Question 2.

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

Solution:
While using a ruler to measure the length of a line segment, we may have the following errors:
(i) Thickness of the ruler
(ii) Angular viewing
These errors can be eradicated by using the divider. So, it is better to use a divider than a ruler, while measuring the length of a line segment.

### Ex 5.1 Class 6 Maths Question 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 AC + CB = AB, then we can be sure that C lies between A and B.]

Solution:
Let us draw a line segment AB = 7 cm and mark a point C such that C lies between A.

Now, measure AC and CB.

AC = 3 cm, CB = 4 cm
AC + CB = 3 cm + 4 cm = 7 cm
But, AB = 7 cm
So, AB = AC + CB

### Ex 5.1 Class 6 Maths Question 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?

Solution:
We have given that, AB = 5 cm, BC = 3 cm
AB + BC = 5 cm + 3 cm = 8 cm
But, AC = 8 cm
Hence, B lies between A and C.

### Ex 5.1 Class 6 Maths Question 5.

Verify, whether D is the mid point of AG.

Solution:
From the given figure, we have
AG = 7 cm – 1 cm = 6 cm
AD = 4 cm – 1 cm = 3 cm
DG = 7 cm – 4 cm = 3 cm
Hence, D is the mid point of AG.

### Ex 5.1 Class 6 Maths Question 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?

Solution:
We have the following figure.

B is the mid-point of AC.
AB = BC       …(i)
C is the mid-point of BD.
BC = CD       …(ii)
From eqs. (i) and (ii), we have
AB = CD         Hence, verified.

### Ex 5.1 Class 6 Maths Question 7.

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

Solution:
Case I.
In ∆ABC

Let AB = 2.5 cm, BC = 4.8 cm and AC = 5.2 cm
AB + BC = 2.5 cm + 4.8 cm = 7.3 cm
Since, 7.3 > 5.2
So, AB + BC > AC
Hence, sum of any two sides of a triangle is greater than the third side.

Case II. In ∆PQR,

Let PQ = 2 cm, QR = 2.5 cm and PR = 3.5 cm
PQ + QR = 2 cm + 2.5 cm = 4.5 cm
Since, 4.5 > 3.5
So, PQ + QR > PR
Hence, sum of any two sides of a triangle is greater than the third side.

Case III. In ∆XYZ,

Let XY = 5 cm, YZ = 3 cm and ZX = 6.8 cm
XY + YZ = 5 cm + 3 cm = 8 cm
Since, 8 > 6.8
So, XY + YZ > ZX
Hence, the sum of any two sides of a triangle is greater than the third side.

Case IV. In ∆MNS,

Let MN = 2.7 cm, NS = 4 cm MS = 4.7 cm
MN + NS = 2.7 cm + 4 cm = 6.7 cm
Since, 6.7 > 4.7
So, MN + NS > MS
Hence, the sum of any two sides of a triangle is greater than the third side.

Case V. In ∆KLM,

Let KL = 3.5 cm, LM = 3.5 cm KM = 3.5 cm
KL + LM = 3.5 cm + 3.5 cm = 7 cm
Since, 7 cm > 3.5 cm
KL + LM > KM
Hence, the sum of any two sides of a triangle is greater than the third side.
Therefore, we conclude that the sum of any two sides of a triangle is never less than the third side.

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