Question

show that the difference of any two sides of a triangle is lesser than the third side

Answer 1

Answer:

Step-by-step explanation:

Consider a right angled triangle for this instance ABC, Let the length of AB = a, BC = b, AC = c,

Apply pythagoras theorem, c^2 = a^2 + b^2,

c^2 - a^2 = b^2,

(c - a)(c + a) = b^2,

c - a = b^2/(c + a),

Since the lengths of sides cannot be negative therefore c + a is positive,

So if c - a = b^2/(c + a),

Then c - a < b^2 and this will definitely imply,

c - a < b which is your proof,

It is true for a right triangle and so is for all other triangles too, just because we don't have any particular theorem or identity which can give proof for other triangles doesn't mean it's false,

Hope it helps

Answer 2

no triangle can be formed with the difference of any two sides greater than or equal to the third side
we have to prove it