Question

Which of the following information is sufficient for construction of a unique triangle?

• A. An equilateral triangle with side 6 cm
• B. A right angled triangle with two other angles measured 40° and 50°
• C. $\overline{AB}$ = 5 cm , $\angle$ A = 35°, $\angle$ C = 75°
• D. An isosceles triangle with equal sides 5 cm

Answer 1

The correct option is A An equilateral triangle with side 6 cm

We can construct a triangle when,
1) Three sides are given
2) Two sides and included angle are given
3)Two angles and included side are given
4) The hypotenuse and one side of a right angled triangle are given.

So here,
a) We are given two angles but the side given is not included, so this information is insufficient.
b) We are given with an equilateral triangle with side 6 cm. Hence, we have all 3 sides of the triangle as 6 cm. Therefore, we can construct a triangle for this condition.
c) We are given all the three angles but length of sides are not given, hence the triangle constructed will not be a unique triangle.
d) We are given two sides as 5 cm, this is insufficient information.