Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $BC = 6 \, cm$,$\angle C = 30^{\circ}$ and $AC - AB = 4 \, cm$.
$A$ triangle $ABC$ can be constructed in which $BC = 6 \, cm$,$\angle C = 30^{\circ}$ and $AC - AB = 4 \, cm$.
(A) The statement is True.
In a triangle,the construction of a triangle $ABC$ is possible if the difference between two sides is less than the third side.
Here,the given difference is $AC - AB = 4 \, cm$ and the third side is $BC = 6 \, cm$.
Since $4 \, cm < 6 \, cm$,the condition $AC - AB < BC$ is satisfied.
Therefore,a triangle $ABC$ can be constructed with the given measurements.
In a triangle,the construction of a triangle $ABC$ is possible if the difference between two sides is less than the third side.
Here,the given difference is $AC - AB = 4 \, cm$ and the third side is $BC = 6 \, cm$.
Since $4 \, cm < 6 \, cm$,the condition $AC - AB < BC$ is satisfied.
Therefore,a triangle $ABC$ can be constructed with the given measurements.
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