Final answer:
The constructed triangle with sides AB = BC = 6cm and angle ∠ABC = 60° is an equilateral triangle, as it satisfies the criteria of having all sides of equal length and all internal angles the same (60° each).
Step-by-step explanation:
When constructing a triangle where sides AB = BC = 6cm and the angle ∠ABC = 60°, the triangle in question is equilateral. To verify this, recall that an equilateral triangle has all three sides of equal length and all internal angles are equal to 60°. Since two sides of the triangle are given as equal (AB = BC) and one of the angles formed between those sides is 60°, it is inherent in the definition of an equilateral triangle that the remaining side (AC) must also be equal to the other two sides, and the remaining angles must also each be 60°.
Therefore, the triangle constructed with the given measurements is an equilateral triangle, which is a specific type of isosceles triangle where not just two, but all three sides and angles are congruent. Equilateral triangles are also known for their symmetry and are a subcategory of regular polygons.