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Two triangles ABC and DBC stand on the same base BC, with A and D on the same side. If ar(ABC) = ar(DBC), then AD is:

Class 9Areas — Figures on the Same BaseGeometry
  • Aparallel to BC
  • Bperpendicular to BC
  • Cequal to BC
  • Dtwice BC

Step-by-Step Solution

Equal-area triangles on the same base and on the same side of it lie between the same parallels, so AD is parallel to BC (converse theorem).
Answer: A) parallel to BC

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