AD and PS are medians of triangles ABC and PQR respectively such that ABD PQS . Prove that ABC PQR .

CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 2 Marks · March 2025 · Standard

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892 Marks · March 2025 · Standard

$AD$ and $PS$ are medians of triangles $ABC$ and $PQR$ respectively such that $\Delta ABD \sim \Delta PQS$. Prove that $\Delta ABC \sim \Delta PQR$.

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Since $\Delta ABD \sim \Delta PQS$
$\therefore \frac{AB}{PQ} = \frac{BD}{QS}$ or $\frac{AB}{PQ} = \frac{2BD}{2QS}$
$\implies \frac{AB}{PQ} = \frac{BC}{QR}$
$\angle B = \angle Q$
$\therefore \Delta ABC \sim \Delta PQR$