Question

Which of the following proportions can be used to prove AE || DK in the proof below? Select all that apply.

Answer 1

Triangle AEF and triangle DFK are similar to each other, this implies that the ratio of the corresponding sides are equal. Hence:
Using the proportions and ratio we have
 the correct statement is:
b

Answer 2

Answer: DA:FA=KE:EF, DF:DA=KF:KE and FA:DA=EF:KE are correct.

Explanation: Since, $\triangle EFA$ and $\triangle KFD$ are similar triangles.

Because, $\angle FAE= \angle FDK$ and $\angle FEA= \angle FKD$ (because EA and KD are parallels. And, $\angle F$ is common angle for these triangles.

Therefore, according to the property of similar triangles.

FE:EK= FA:AD, FE:FK=FA:FD and DF:DA=KF:KE .

Thus, first, second and third options are correct.