Question

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

the pictures in order are
a
b
c
d
and the last picture is a figure if an awnser is missing please tell me if that one is the correct one

Answer 1

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.