In the given figure AD = 5 cm, AB = 15 cm, AE = 6 cm, AC = 24 cm. Then which of the following is correct ?

DE = BC

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$D E ∥ B C$

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AB = AC

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$D E ∦ B C$

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Solution

The correct option is D
$D E ∦ B C$

In the given figure:

$\frac{A D}{A B}$ = $\frac{5 c m}{15 c m}$ = $\frac{1}{3}$ ;

$\frac{A E}{A C}$ = $\frac{6 c m}{24 c m}$ = $\frac{1}{4}$ ;

$∵$ $\frac{A D}{A B}$ $\neq$ $\frac{A E}{A C}$ ;

$∴$ By converse of Basic Proportionality Theorem (If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side)

we can say that $D E ∦ B C$

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