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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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