A student tries to draw triangle XYZ with the following measurements: XY = 5\,cm, XZ = 5\,cm and ∠Y=40∘.
(i) Perform the construction(s) that are possible with the given data. Show all arcs and construction lines.
(ii) How many non-congruent triangles can be obtained? Give reasons for your answer.
(iii) Explain, with reference to triangle congruence conditions, why the information provided does or does not guarantee a unique triangle.
(iv) State a minimal additional piece of information that would make the construction lead to exactly one triangle, and explain why this extra information is sufficient.