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In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by :

  1. SAS

  2. ASA

  3. AAA

  4. RHS

Similarity

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Answer

In △ CBA and △ ABD,

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by : Similarity, Concise Mathematics Solutions ICSE Class 10.

⇒ ∠CAB = ∠ADB (Both equal to 90°)

⇒ ∠CBA = ∠DBA (Common angles)

Since, two angles of two triangles are equal so third angle of both the triangle will also be equal.

⇒ ∠ACB = ∠DAB.

∴ △ CBA ~ △ ABD (By A.A.A. postulate)

Hence, Option 3 is the correct option.

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