Let's consider the facts at hand:
- By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
- ∠BEC = ∠DFC
- Sides BE = DF
Based on the diagram, triangles BCE and triangles DCF are similar
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
Definitions of Theorem I used:
- Vertical Angle Theorem: opposite angles of two intersecting lines must be equal
- Angle-Angle Theorem: if two angles of both triangles are equal, then the given triangles must be similar