Question

In which of the following cases one cannot construct a unique triangle without any additional information?

• A. All three angles are given
• B. All three sides are given
• C. Two sides and included angle are given
• D. Two angles and the included side is giv

Answer 1

The correct option is A All three angles are given

In option A: When all the three sides are given
A unique triangle can be constructed when the three sides of a triangle are given using the Side Side Side property.

In option B: All three angles are given
When all the three angles are given, then the constructed triangle will not be unique. Therefore, in that case, the desired triangle cannot be constructed.

In option C: Two sides and included angle are given
A unique triangle can be constructed when two sides and an angle are included using the Side Angle Side criterion.

In triangle D: Two angles and the included side is given
A unique triangle can be constructed when two angles and the included side are given using the Angle Side Angle criterion.

Option B is correct.