Question

Which of the following information are needed to draw a unique $\Delta ABC$?

• A. Length of AB and AC only
• B. Length of AB, AC and BC
• C. $\angle A$, $\angle B$ and $\angle C$
• D. AB, BC and $\angle C$

Answer 1

The correct option is B

Length of AB, AC and BC

1. We need three measurements to construct a triangle. The lengths of sides AB, AC and BC are required to draw a unique $\Delta ABC$.
2. With the set of measurements of three angles, we can construct infinite triangles. Example: All equilateral triangles have the ${60}^{\circ }$ between any two sides. The sides of the equilateral triangles can be 3 cm, 3 cm and 3 cm or 5 cm, 5 cm and 5 cm or 7 cm, 7 cm and 7 cm. Hence with three angles, an infinite number of triangles can be drawn.
3. Similarly, option D won’t give a unique triangle. Only two sides and an included angle can make a unique triangle.