Question

Which of the following sets of information is not sufficient for the formation of a unique triangle ABC?

• A. $AB=6cm,BC=6cm,\text{and}\angle ABC={60}^{\circ }$
  
• B. $\angle ABC={60}^{\circ },\angle ACB={60}^{\circ },\text{and}\angle BAC={60}^{\circ }$
  
• C. $AB=6cm,\angle ABC={60}^{\circ },\text{and}\angle BAC={60}^{\circ }$
• D. $AB=6cm,BC=6cm,\text{and}CA=6cm$
  

Answer 1

The correct option is B $\angle ABC={60}^{\circ },\angle ACB={60}^{\circ },\text{and}\angle BAC={60}^{\circ }$


A unique triangle can be formed when
a) the lengths of the three sides of a triangle are given.
(This implies that option A has sufficient information to draw a unique triangle.)
b) the lengths of two sides and the measure of one interior angle of a triangle is given.
(This implies that option B has sufficient information to draw a unique triangle.)
c) the length of one side and the measure of two interior angles of a triangle is given.
(This implies that option C has sufficient information to draw a unique triangle.)

But more than one triangle can be formed when the information about the three interior angles of a triangle is given.
(This implies that option D does not have sufficient information to draw a unique triangle.)

$\to$ Option D is correct.