If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
Given:
Each angle of a triangle is less than the sum of the other two.
To do:
We have to show that the triangle is acute angled.
Solution:
Let in a $\triangle ABC$, $\angle A < \angle B + \angle C$
This implies,
$\angle A + \angle A < \angle A + \angle B + \angle C$
$2\angle A < 180^o$
$\angle A < 90^o$
Similarly,
$\angle B < 90^o$
$\angle C < 90^o$
Hence, each angle of the triangle is an acute angle.
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