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Prove that the difference between any …

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Prove that the difference between any two sides of a triangle is less than its third side.

Posted by Tanu Priya 7 years, 10 months ago

Sia ? 4 years, 6 months ago

Let suppose the triangle ABC as in figure attached:

Here we have cut off side AC at point D such that AD=AB and join BD.

As AD=AB, so ∠2=∠4

∠1>∠4 because Exterior angle is always greater than respective interior angle.

Similarly, ∠2>∠3.

Therefore ∠1>∠3 and BC>DC as size opposite to greater angle are also greater in length.

now, ⇒BC>DC

⇒BC>AC-AD as DC=AC-AD

⇒BC>AC-AB because AD=AB

Similarly, BC-AC<AB and BC-AB<AC

Hence it is proved that either side of triangle is always greater than difference of remaining two sides.

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