Assertion $(A): A B C D$ is a trapezium with $D C \| A B$. $E$ and $F$ are points on $A D$ and $B C$

Question

Assertion $(A): A B C D$ is a trapezium with $D C \| A B$. $E$ and $F$ are points on $A D$ and $B C$ respectively, such that $E F \| A B$. Then $\frac{A E}{E D}=\frac{B F}{F C}$.\ Reason (R) : Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.\

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(b): Given, $A B C D$ is a trapezium, $D C \| A B$.\ $E$ and $F$ are points on $A D$ and $B C$ respectively, such that $E F \| A B$\ Construct the line $A C$ such the point $L$ lies on it\ In $	riangle A C D, E L \| D C$\ $	herefore \quad \frac{A E}{E D}=\frac{A L}{L C}$ (By B.P.T.) In $	riangle A B C, F L \| A B$\ $	herefore \quad \frac{A L}{L C}=\frac{B F}{F C}$ (By B.P.T.) From (i) and (ii), $\frac{A E}{E D}=\frac{B F}{F C}$ From (i) and (ii), $\frac{A E}{E D}=\frac{B F}{F C}$\ Hence, both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).\