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△ABC is equilateral. D, E, F lie on AB, BC, CA with AD = BE = CF. What kind of triangle is DEF?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • ARight-angled
  • BIsosceles but not equilateral
  • CEquilateral
  • DScalene

Step-by-Step Solution

Each of △ADF, △BED, △CFE has one side equal to AD, another equal to (side − AD), and a 60° angle between them. By SAS all three are congruent, so DF = ED = FE.
Answer: C) Equilateral

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