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A line divides two sides of a triangle so that AD = 2, DB = 3, AE = 4, EC = 6. Is DE parallel to BC?

Class 10Basic Proportionality TheoremGeometry — Similarity

AYes, because $\frac{A D}{D B} = \frac{A E}{EC}$
BNo, because the ratios differ
CCannot be determined
DOnly if the triangle is equilateral

Step-by-Step Solution

\frac{A D}{D B} = \frac{2}{3}

and

\frac{A E}{EC} = \frac{4}{6} = \frac{2}{3}

. Equal ratios, so by the converse of BPT,

D E ∣∣ BC

.

Answer: A) Yes, because

\frac{A D}{D B} = \frac{A E}{EC}

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