Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $AB = 5 \, cm$,$\angle A = 45^{\circ}$ and $BC + AC = 5 \, cm$.

(FALSE) The statement is False.
According to the triangle inequality theorem,the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.
In this case,we are given $AB = 5 \, cm$ and $BC + AC = 5 \, cm$.
This implies $BC + AC = AB$,which violates the triangle inequality theorem.
Therefore,a triangle with these dimensions cannot be constructed.