Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of △ PQR…
CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 5 Marks · March 2025 · Standard
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1195 Marks · March 2025 · Standard
Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of $\triangle PQR$. Show that $\triangle ABC \sim \triangle PQR$.
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Sol. Correct figure In $\triangle ABD$ and $\triangle PQM$ $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AD}{PM}$ (given) $\frac{AB}{PQ} = \frac{2BD}{2QM} = \frac{AD}{PM}$ $\frac{AB}{PQ} = \frac{BD}{QM} = \frac{AD}{PM}$ $\therefore \triangle ABD \sim \triangle PQM$ $\therefore \angle B = \angle Q$ In $\triangle ABC$ and $\triangle PQR$ $\frac{AB}{PQ} = \frac{BC}{QR}$ and $\angle B = \angle Q$ $\triangle ABC \sim \triangle PQR$
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