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ICSE Class 10 Mathematics Question 27 of 49

Multiple-Choice Questions — Question 27

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Question 27

In the adjoining diagram, ST is not parallel to PQ. The necessary and sufficient conditions for △ PQR ~ △ TSR is :

  1. ∠PQR = ∠STR

  2. ∠QPR = ∠TSR

  3. ∠PQR = ∠TSR

  4. ∠PRQ = ∠RST

In the adjoining diagram, ST is not parallel to PQ. The necessary and sufficient conditions for △ PQR ~ △ TSR is : Maths Competency Focused Practice Questions Class 10 Solutions.
Answer

Given,

△ PQR ~ △ TSR.

From figure,

⇒ ∠PRQ = ∠SRT (Common angle)

The order of vertices of two similar triangles are written in such a way that the corresponding vertices occupy the same position.

∴ ∠PQR = ∠TSR

∴ △ PQR ~ △ TSR (By A.A. axiom)

Hence, Option 3 is the correct option.