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Triangles
RD Sharma
CBSE
Grade 10
Question:
If $\Delta ABC \sim \Delta PQR$ and $AD, PS$ are altitudes of $\Delta ABC$ and $\Delta PQR$ respectively, prove that $\dfrac{AB}{PQ} = \dfrac{AD}{PS}$.
Step-by-Step Solution
Key Concept: In $\Delta ABD$ and $\Delta PQS$, $\angle B = \angle Q$ and $\angle ADB = \angle PSQ = 90^\circ \Rightarrow \Delta ABD \sim \Delta PQS \Rightarrow \dfrac{AB}{PQ} = \dfrac{AD}{PS}$.
In $\Delta ABD$ and $\Delta PQS$: $\angle B = \angle Q$ (as $\Delta ABC \sim \Delta PQR$) $\angle ADB = \angle PSQ = 90^\circ$ (Altitudes) [1.0 Mark] By AA similarity, $\Delta ABD \sim \Delta PQS$. [0.5 Mark] $\dfrac{AB}{PQ} = \dfrac{AD}{PS}$. Proved! [0.5 Mark]
--- 🎯 Official CBSE Marking Scheme: Proving $\Delta ABD \sim \Delta PQS$ by AA: 1.5 Marks Writing corresponding side ratio: 0.5 Mark
Correct Answer:
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