Given: D is the midpoint of segment BF, segment BC || segment EF

Prove: ΔBDC ≅ ΔFDE

ΔBDC ≅ ΔFDE

Step-by-step explanation:

The proof is given below

To prove ΔBDC ≅ ΔFDE

Statements                           reasons

1). BC║EF                         -  Given

2).  D is the mid point         - Given

3). BD = DF                        - Definition of midpoint

4). <BDC = <FDE               - Vertically opposite angles are equal

5).  <CBD = <DFE              - alternate interior angles of parallel lines are                                      

                                               congruent

6). ΔBDC ≅ ΔFDE                 ASA rule

Therefore ΔBDC ≅ ΔFDE. Hence the proof.