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Question

Difference of two sides of a triangle is always _______ than the third side.

A
Greater
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B
Lesser
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C
Equal
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D
Not sure
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Solution

The correct option is B Lesser
Difference of two sides of a triangle is always lesser than the third side.
Proof:

Start with the Triangle Inequality Theorem which is, the sum of any two sides of a triangle must be greater than the third. Stated algebraically:
Let A, B and C be the sides of the triangle.
A < B + C
B < A + C
C < A + B

1. Subtract B from both sides, then A - B < C
2. Subtract C from both sides, then B - C < A
3. Subtract A from both sides, then C - A < B

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