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Mathematics

In the given figure :

  1. △ ABE ~ △ ADE

  2. △ ADE ~ △ ABC

  3. △ ADE ~ △ BAC

  4. △ ADE ~ △ CAB

In the given figure : Similarity, Concise Mathematics Solutions ICSE Class 10.

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Answer

From figure,

⇒ ∠BAE = x (let)

⇒ ∠DAB = ∠EAC = y (let)

⇒ ∠AED = ∠ACB = z (let)

⇒ ∠DAE = ∠DAB + ∠BAE = y + x

⇒ ∠BAC = ∠BAE + ∠EAC = x + y

⇒ ∠DAE = ∠BAC = x + y

In △ ABC and △ ADE,

⇒ ∠DAE = ∠BAC (Proved above)

⇒ ∠AED = ∠ACB (Both equal to z)

∴ △ ADE ~ △ ABC (By A.A. axiom)

Hence, Option 2 is the correct option.

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