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

0 votes
1 view
asked Jun 12 in Class VII Maths by muskan15 (-3,437 points)

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

Please log in or register to answer this question.

1 Answer

0 votes
answered Jun 12 by aditya23 (-2,140 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.

Related questions

0 votes
1 answer