ABC is an equilateral triangle AD and BE are perpendiculars to BC and AC respectively.

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asked 6 days ago in Class VII Maths by muskan15 (-2,499 points)

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

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1 Answer

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answered 6 days ago by aditya23 (-854 points)

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.

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