Question

Assertion :If in a $△ABC$, a line $DE\parallel BC$, intersects AB in D and AC in E, then $\frac{AB}{AD}=\frac{AC}{AE}$. Reason: If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

For Assertion (A)
Since $DE\parallel BC$

$\therefore$ by Thale's Theorem

$\frac{AD}{DB}=\frac{AE}{EC}\Rightarrow \frac{DB}{AD}=\frac{EC}{AE}$

$\Rightarrow 1+\frac{DB}{AD}=1+\frac{EC}{AE}$

$\Rightarrow \frac{AD+DB}{AD}=\frac{AE+EC}{AE}\Rightarrow \frac{AB}{AD}=\frac{AC}{AE}$

$\therefore$ Assertion (A) is true since reason gives Assertion.