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In △ABC, D is the mid-point of BC. BE and CF are perpendiculars from B and C to line AD (produced). Why is BE = CF?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • A△BDE ≅ △CDF by SAS
  • BBecause AB = AC
  • C△BDE ≅ △CDF by AAS
  • D△ABE ≅ △ACF by SSS

Step-by-Step Solution

∠BED = ∠CFD = 90°, ∠BDE = ∠CDF (vertically opposite) and BD = CD (opposite the right angles). AAS gives the congruence, then BE = CF by CPCT.
Answer: C) △BDE ≅ △CDF by AAS

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