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A line cuts side AB of triangle ABC at D and side AC at E. Given AD = 4 cm, DB = 8 cm, AE = 5 cm, EC = 9 cm, decide whether DE || BC.

Class 10Basic Proportionality TheoremGeometry — Similarity

ANo, since $\frac{4}{8}$ is not equal to $\frac{5}{9}$
BYes, since $\frac{4}{8} = \frac{5}{9}$
CYes, since AD < AE
DCannot be decided

Step-by-Step Solution

\frac{A D}{D B} = \frac{4}{8} = \frac{1}{2} = 0.5, \frac{A E}{EC} = \frac{5}{9} = 0.556

. Unequal, so

D E

is not parallel to

BC

.

Answer: A) No, since

\frac{4}{8}

is not equal to

\frac{5}{9}

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