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Triangles
RD Sharma
CBSE
Grade 10
Question:
In $\Delta ABC$, $D$ and $E$ are points on sides $AB$ and $AC$ respectively. If $AD = 2\text{ cm}, DB = 3\text{ cm}, AE = 3.6\text{ cm}$ and $EC = 5.4\text{ cm}$, then: (a) $DE \parallel BC$ (b) $DE$ is not parallel to $BC$ (c) $DE \perp BC$ (d) $DE = BC$
Step-by-Step Solution
Key Concept: $\dfrac{AD}{DB} = \dfrac{2}{3}$. $\dfrac{AE}{EC} = \dfrac{3.6}{5.4} = \dfrac{2}{3}$. Since ratios are equal, by converse of BPT, $DE \parallel BC$.
$\dfrac{AD}{DB} = \dfrac{2}{3}$ and $\dfrac{AE}{EC} = \dfrac{3.6}{5.4} = \dfrac{2}{3}$. By converse of BPT, $DE \parallel BC$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Applying converse of BPT: 1.0 Mark
Correct Answer:$DE \parallel BC$
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