1.

1. If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angle.

Answer»

Let,
ABC is a triangle.

Then,
ANGLE A+angleB+angleC=180°---------------(1)

If angle A + angle B < angle C

Then,

using equation (1),

we GET,

angle C + angle C < 180°
=> 2 angle C < 180°
=> angle C < 180°/2
=> angle C < 90°

Similarly , we get,
angle A < 90° and angle B < 90°

If each angle of a triangle is less than 90°,it is KNOWN as acute triangle.

Hence,ABC is a acute triangle.

SHOWED.


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