Given: BC = DC and BL ⊥ AD and DM ⊥ CM

To prove: BL=CM

Proof:

In ∆BLD and ∆CMD,

∠BLD = ∠CMD = 90° … given

∠BLD = ∠MDC … vertically opposite angles

BD = DC … given

Thus by AAS property of congruence,

∆BLD ≅ ∆CMD

Hence, we know that, corresponding parts of the congruent triangles are equal

∴ BL = CM