Question

50 Points: Name the similar triangles & Prove the similarity with details

Answer 1

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