Question

In the following figure, BL = CM.

Prove that AD is a median of triangle ABC.

Answer 1

In  ΔDLB and  ΔDMC,
BL = CM                     ...( given )
∠DLB = ∠DMC           ...( Both are 90° )
∠BDL = ∠CDM           ....( vertically opposite angels )
∴ ΔDLB ≅ ΔDMC       ....( AAS congruence criterion )
BD = CD                      ....( cpct )
Hence, AD is the median of ΔABC.