Question

If $AB=3$ centimeters, $AC=5$ centimeters and $\angle B={30}^{\circ }$, why can $\Delta ABC$ not be constructed uniquely with $AC$ as base?

• A. The other two angles are not given
• B. The vertex B cannot be uniquely located
• C. Two sides and the included angle is given
• D. The vertex A coincides with the vertex C

Answer 1

The correct option is B The vertex B cannot be uniquely located

Two sides and an included angle is given, which means we could draw a triangle using SAS criterion. However, SAS criterion requires the measurement of the included angle between the two sides which has a common vertex.

$\angle B$ is given and the sides are $\overline{AB}$ and $\overline{AC}$ which means that $\angle B$ is not the included angle. Hence, we cannot construct a unique triangle with AC as the base.