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Example:-

Which of the following can be the sides of a right triangle?
(i) 2.5 cm,6.5 cm, 6 cm.
(ii) 2 cm, 2 cm, 5 cm

Solution:
i) 2.5cm, 6.5cm, 6cm

we see that
2
2
2
(2.5) +6 =6.25+36=42.25= (6.5)
Therefore, the given lengths can be the sides of a right triangle. Also, the angle between the
lengths, 2.5 cm and 6 cm is a right angle.

ii) 2 cm, 2 cm, 5 cm.

Here 2+ 2= 4 < 5, so sum of two sides less than third side. So this is not a triangle.

Example:

Angles Q and R of a triangle PQR are 25º and 65º.

Write which of the following is true:
2
2
2
(i) PQ + QR = RP
2
2
2
(ii) PQ + RP = QR
2
2
2
(iii) RP + QR = PQ

Solution
From angle property of triangle
0
Angle P = 180 -25-65=90
So triangle PQR is right angle at P
So

2
2
2
PQ + RP = QR