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In $\triangle ABC$, points D and E lie on AB and AC respectively. If $\dfrac{AD}{DB}=\dfrac{AE}{EC}$, then which conclusion is correct? 
A$DE \parallel BC$
B$DE \perp BC$
C$DE$ bisects $\angle A$
D$AB=AC$
Answer & Solution
Correct answer: A. $DE \parallel BC$
This is the converse of the Basic Proportionality Theorem. If a line divides two sides of a triangle in the same ratio, then that line is parallel to the third side. Hence $DE \parallel BC$.
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