Triangle DEF is to be drawn with DE = 6 ,cm, DF = 8 ,cm and ( E ) equal to (50^ )
MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
Triangle DEF is to be drawn with DE = 6\,cm, DF = 8\,cm and ∠E equal to 50∘.
(i) State the congruence condition that guarantees a unique triangle when two sides and an angle are given.
(ii) Is the information provided for triangle DEF sufficient to guarantee only one possible triangle? Give a detailed explanation supported by a clear ruler–compass sketch.
(iii) If more than one triangle can be constructed with the given measurements, draw both possible triangles and label them clearly. If only one triangle is possible, justify why no second triangle can be drawn.