AD and PS are angle bisectors of ∠ A and ∠ P of triangles ABC and PQR. If ABC PQR , prove that ACD PRS .

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

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902 Marks · March 2025 · Standard

AD and PS are angle bisectors of $\angle A$ and $\angle P$ of triangles ABC and PQR. If $\Delta ABC \sim \Delta PQR$, prove that $\Delta ACD \sim \Delta PRS$.

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$\Delta ABC \sim \Delta PQR$
$\therefore \angle BAC = \angle QPR$
$\implies \frac{1}{2} \angle BAC = \frac{1}{2} \angle QPR$
$\implies \angle 2 = \angle 4$ and $\angle C = \angle R$
$\therefore \Delta ACD \sim \Delta PRS$