Question

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.

Assertion (A): $\text{If}BC||EF\text{and}FG||CD\text{then,}\frac{AE}{AB}=$$\frac{AG}{AD}$.

Reason (R): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
[ 1 mark ]

(A) Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
(B) Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).
(C) Assertion (A) is true, but reason (R) is false.
(D) Assertion (A) is false, but reason (R) is true.

Answer 1

Answer: (A)

$\text{In}\Delta ABC,$

$EF\parallel BC$

$\therefore \frac{AE}{AB}=\frac{AF}{AC}....\left(1\right)\text{(Basic proportionality theorem)}$

$\text{In}\Delta ACD,$

$FG\parallel CD$

$\therefore \frac{AF}{AC}=\frac{AG}{AD}....\left(2\right)\text{(Basic proportionality theorem)}$

$\text{From 1 \& 2,}$

$\frac{AE}{AB}=\frac{AF}{AC}=\frac{AG}{AD}$

$\Rightarrow \frac{AE}{AB}=\frac{AG}{AD}$

Hence, both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
[1 mark]