Question

Can you prove triangle BAC is similar to triangle DFE ? Justify your answer.

Answer 1

you can use side-angle-side postulate 

Answer 2

By AA property of similarity, triangles BAC and DFE are similar.

Explanation:

Given information: AC║FE and AB║FD.

If a transversal line intersect two parallel lines, then the corresponding angles are equal.

In triangle BAC and triangle DFE

`\angle ABC=\angle FDE` (corresponding angles)

`\angle ACB=\angle FED` (corresponding angles)

Two corresponding angles of triangles are equal. So, by AA property of similarity both triangles BAC and DFE are similar.

`\triangle BAC\sim \triangle DFE`

Hence proved.