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Triangles

Which of the ...

Question

Which of the following is true for the given triangle?

AC = BC

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AC < BC

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AC > BC

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AC = BC = AB

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Solution

The correct option is C AC > BC
In $△ A B C$ , we have
$∠ A$ + $∠ B$ + $∠ C$ = $180^{\circ}$
(Angle sum property of a triangle)
=> $30^{\circ}$ + $60^{\circ}$ + $∠ B$ = $180^{\circ}$
=> $∠ B$ = $90^{\circ}$
$∴$ The largest angle in the given triangle is $∠ B$ .
We know,
Side opposite to the biggest angle will be the largest of the three.
Side opposite to $∠ B$ is AC
Therefore, AC is the largest side of
$△$ ABC
Hence, AC > BC

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