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Abc is an Equilateral Triangle, Ad and Be Are Perpendiculars to Bc and Ac Respectively. Prove That: (I) Ad = Be (Ii)Bd = Ce - Mathematics

Sum

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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Solution

In Δ ABC,

AB = BC = CA,

AD ⊥ BC, BE ⊥ AC.

Proof: In Δ ADC and Δ BEC

∠ADC = ∠BEC ...........(each 90°)

∠ACD = ∠BCE ..............(common)

and AC = BC ............(sides of an equilateral triangle)

∴ Δ ADC ≅ Δ BEC ...........(A.A.S. Axiom)

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

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

Hence proved.

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
  Is there an error in this question or solution?
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 13
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