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Answer :

(I) In first figure,

It is an equalatral triangle

Sum of two side = 5 + 5 = 10

10 > 5
Hence, the sum of any two sides of a triangle is greater than the third side.

(II) In second figure ,

Sum of two side = 5 + 5 = 10 , 5 + 3 = 8 , 5 + 3 = 8

\(\therefore \) 10 > 3, 8 > 5 , 8 > 5

Hence, the sum of any two sides of a triangle is greater than the third side.

(III) In third figure,

Sum of two side = 6 + 10 = 16 , 8 + 10 = 18 , 6 + 8 = 14

\(\therefore \) 16 > 8, 18 > 6, 14 > 10

Hence, the sum of any two sides of a triangle is greater than the third side.

(IV) In forth figure,

Sum of two side = 6 + 7 = 13 , 7 + 6 = 13 , 6 + 6 = 12

\(\therefore \) 13 > 6, 13 > 6, 12 > 7

Hence, the sum of any two sides of a triangle is greater than the third side.

(IV) In fifth figure,

Sum of two side = 12 + 5 = 17 , 13 + 5 = 18 , 12 + 13 = 25

\(\therefore \) 17 > 13, 18 > 12, 25 > 5

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 always greater than the third side.

- Q.1 What is the disadvantage in comparing line segments by mere observation?
- Q.2 Why is it better to use a divider than a ruler, while measuring the length of a line segment?
- Q.3 Draw any line segment, say \(\overline {AB} \). 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]
- Q.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?
- Q.5 Verify, whether D is the mid point of\(\overline {AG} . \)
- Q.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?

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