Page 165 - Start Up Mathematics_5

Property 2

The sum of the lengths of any two sides of a triangle is greater than the P
length of the third side.

PQ + QR > PR or PQ + PR > QR or QR + PR > PQ
If the measure of angles is not given but the measure of sides is given, then
using this property we can find out whether a triangle can be formed or not. Q R

Example 2: Given the measure of three sides, find out whether a triangle can be formed
or not.

(a) 6 cm, 4 cm, 5 cm (b) 3 cm, 10 cm, 6 cm
Solution: (a) The three sides are 6 cm, 4 cm and 5 cm.

6 cm + 4 cm = 10 cm > 5 cm
6 cm + 5 cm = 11 cm > 4 cm
4 cm + 5 cm = 9 cm > 6 cm

So, a triangle can be formed.
(b) The three sides are 3 cm, 10 cm and 6 cm.
3 cm + 10 cm = 13 cm > 6 cm

3 cm + 6 cm = 9 cm < 10 cm
As the sum of two sides 3 cm and 6 cm is less than the third side 10 cm,
a triangle cannot be formed.

EXERCISE 12.3

1. Identify the types of triangles and write their names.

A P Q
90°
80°
(a) (b)

60° 40°
B C R
___________________ ___________________

D S

(c) (d) 3 cm
3 cm 3 cm 3 cm

U 4 cm T
E 3 cm F
___________________ ___________________

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