CBSE Class 10 Mathematics Standard 2026: question 34(B)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. (i) Since $△ABC\sim △PQR$, corresponding angles are equal:
   $$\angle A=\angle P\text{...(1)}$$

   ½ mark

2. (i) Corresponding sides are proportional:
   $$\frac{AB}{PQ}=\frac{AC}{PR}$$

   $CM$ and $RN$ are medians, so $M$ is the midpoint of $AB$ and $N$ is the midpoint of $PQ$. Hence $AB=2AM$ and $PQ=2PN$:
   $$\frac{2AM}{2PN}=\frac{AC}{PR}\Rightarrow \frac{AM}{PN}=\frac{AC}{PR}\text{...(2)}$$

   1½ marks

3. (i) In $△AMC$ and $△PNR$, $\angle A=\angle P$ from (1), and the sides containing these angles are proportional from (2).

   By the SAS similarity criterion, $△AMC\sim △PNR$.

   ½ mark

4. (ii) Since $△ABC\sim △PQR$:
   $$\angle B=\angle Q\text{...(3)}$$

   ½ mark

5. (ii) Also
   $$\frac{AB}{PQ}=\frac{BC}{QR}$$

   As $AB=2MB$ and $PQ=2NQ$ (because $M$ and $N$ are midpoints):
   $$\frac{2MB}{2NQ}=\frac{BC}{QR}\Rightarrow \frac{MB}{NQ}=\frac{BC}{QR}\text{...(4)}$$

   1½ marks

6. (ii) In $△CMB$ and $△RNQ$, $\angle B=\angle Q$ from (3), and the sides containing these angles are proportional from (4).

   By SAS similarity, $△CMB\sim △RNQ$.

   ½ mark

Answer: (i) $△AMC\sim △PNR$ (SAS); (ii) $△CMB\sim △RNQ$ (SAS)

Revise the chapter

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