If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
Proof
Let ABC be a triangle,
Now,
< +___________________ (i)
< +___________________ (ii)
< +___________________ (iii)
2 < ++ [From equation (i)]
2 < 180° [Sum of angles of triangle]
< 90° ________________ (a)
Similarly,
< 90°__________________ (b)
< 90°__________________ (c)
From equation (a), (b) and (c), each angle is less than 90°
Therefore triangle is an acute angled Proved.