Question

If $AB=3$ centimeters, $AC=5$ centimeters and $\angle B=30°$, why can $△ABC$ not be constructed uniquely with $AC$ as base?

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

Answer 1

The correct option is D 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.