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ICSE Class 10 Mathematics Question 2 of 21

Solved 2024 Question Paper ICSE Class 10 Mathematics — Question 15

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15
Question

Question 1(xv)

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.
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.