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In $\triangle ABC$, a line through points D on AB and E on AC is drawn parallel to BC. According to the Basic Proportionality Theorem, which relation must hold? 
A$\dfrac{AD}{AB}=\dfrac{DE}{BC}$
B$\dfrac{AD}{DB}=\dfrac{AE}{EC}$
C$\dfrac{AB}{AC}=\dfrac{DB}{EC}$
D$AD=AE$
Answer & Solution
Correct answer: B. $\dfrac{AD}{DB}=\dfrac{AE}{EC}$
The Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, then it divides those two sides in the same ratio. Therefore, with $DE \parallel BC$, we get $\dfrac{AD}{DB}=\dfrac{AE}{EC}$.
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