Question

Question 14
D and E are the mid-points of the sides AB and AC, respectively, of $\Delta ABC.DE$ is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(a) $\angle DAE=\angle EFC$
(b) $AE=EF$​​​​​​​
(c) $DE=EF$​​​​​​​
(d) $\angle ADE=\angle ECF$​​​​​​​

Answer 1

In $\Delta ADE$ and $\Delta CFC$, suppose DE = EF

Now, AE = CE [Since, E is the mid-point of AC]

Suppose DE = EF

And $\angle AED=\angle FEC$ [Vertically opposite angles]

$\therefore \Delta ADE\cong \Delta CFE$ [ By SAS congruence rule]

AD = CF [By CPTC rule]

And $\angle ADE=\angle CFE$ [ By CPCT]

Hence, AD ∥ CF [ Since, alternate interior angles are equal]

Therefore, we need an additional information which id DE = EF