Answer:
Triangle A
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
1) Triangle A: All angles measure 60°
In this case we could have several similar triangles with the corresponding angles congruent and corresponding sides proportional .
therefore
Triangle A is not a unique triangle
2) Triangle B: All sides have length 6 cm
If all sides have length 6 cm, then is an equilateral triangle
In this case Triangle B is a unique triangle
3) Triangle C: Two sides have length 6 cm, and the included angle measures 60°
With the law of cosines calculate the length of the third side and with the law of sines calculate the measure of the other two interior angles
Is an equilateral triangle with all sides have length 6 cm
In this case Triangle C is a unique triangle
4) Triangle D: Base has length 6 cm, and base angles measure 50°
With the two base angles calculate the measure of the third angle, and with the law of sines determine the length side of the other two congruent sides
Is an isosceles triangle with base angles measure 50°, vertex angle measure 80° and base has length of 6 cm.
In this case Triangle D is a unique triangle
