CBSE Class 10 Mathematics Basic 2024: question 34(a)

Hints

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Step-by-step solution

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1. Figure: $△ABC$ with median AD (D mid-point of BC) and $△PQR$ with median PM (M mid-point of QR).

   ½ mark

2. Given: $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AD}{PM}$, AD and PM medians. To prove: $△ABC\sim △PQR$.

   1 mark

3. Since D and M are mid-points, $BD=\frac{1}{2}BC$, $QM=\frac{1}{2}QR$. So $\frac{AB}{PQ}=\frac{\frac{1}{2}BC}{\frac{1}{2}QR}=\frac{AD}{PM}\Rightarrow \frac{AB}{PQ}=\frac{BD}{QM}=\frac{AD}{PM}$

   1 mark

4. $\therefore △ABD\sim △PQM$ [SSS similarity criterion]

   ½ mark

5. $\Rightarrow \angle B=\angle Q$ [corresponding angles of similar triangles]

   ½ mark

6. In $△ABC$ and $△PQR$: $\frac{AB}{PQ}=\frac{BC}{QR}$ [given] and $\angle B=\angle Q$ [proved]. $\therefore △ABC\sim △PQR$ [SAS similarity criterion].

   1½ marks

Answer: $△ABC\sim △PQR$ (via $△ABD\sim △PQM$ by SSS, then SAS).

Revise the chapter

• Chapter: Triangles (notes, formulas, where marks are lost and every past question)