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Mathematics

In the given diagram, ∆ABC ∼ ∆PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then:

  1. ∆ABC ∼ ∆PQS

  2. ∆ABD ∼ ∆PQS

  3. ∆ABD ∼ ∆PSR

  4. ∆ABC ∼ ∆PSR

In the given diagram, ∆ABC ∼ ∆PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then: ICSE 2024 Maths Solved Question Paper.

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ICSE 2024

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Answer

Given,

∆ABC ∼ ∆PQR

∴ ∠A = ∠P

⇒ ∠A2=∠P2\dfrac{∠A}{2} = \dfrac{∠P}{2}

⇒ ∠BAD = ∠QPS

∠B = ∠Q [∵ ∆ABC ∼ ∆PQR]

In ∆ABD ∼ ∆PQS,

⇒ ∠BAD = ∠QPS

⇒ ∠B = ∠Q

∴ ∆ABD ∼ ∆PQS (By A.A. axiom)

Hence, Option 2 is the correct option.

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