Abc Is Equilateral Triangle Ad And Be Are Perpendiculars To Bc And Ac Respectively

ABC is an equilateral triangle, AD and BE are perpendiculars to BC and AC respectively. Prove that: (i) AD = BE (ii) BD = CE


In △ ABC,

AB = BC = CA,

AD ⊥ BC, BE ⊥ AC,

Proof: In △ ADC and △ BEC

∠ADC = ∠BEC (each 90°)

∠ACD = ∠BCE (common)

and AC = BC (Sides of an equilateral triangle)

∴ △ ADC ≅ △ BEC (A.A.S. Axiom)

Hence, (i) AD = BE (c.p.c.t)

And (ii) BD = CE (c.p.c.t)

Hence proved.