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Question

# If two sides of a triangle are unequal, the greater side has the greater angle opposite to it. State whether the given statement is true or false.

A

True

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B

False

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Solution

## The correct option is A True Let consider a triangle ABC in which AB > AC. From AB, cut AD = AC. Join C and D. In ΔACD: AC = AD (by construction) --------(1) ∠ACD = ∠ADC (Angle opposite to equal side) --------(2) In ΔBDC Ext . ∠ADC > ∠B (Ext. angle always greater than each of its interior opposite angles) --------(3) ∠ACD > ∠B ------------ From (2) and (3) Hence, ∠ACB > ∠B Therefore, ∠ACB > ∠ACD > ∠B Thus, given statement is true.

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