Part 1: Use the transformations to prove congruency

Answer:
See Explanation
Step-by-step explanation:
[tex] \overline{CB} ||\overline {ED}... (GIVEN) \\
\& BD\:\&\: CE \: are \: transversals\\
\angle CBF\cong \angle EDF.. (alternate \: \angle 's) \\
\overline{CB} \cong \overline {ED}..... (GIVEN) \\
\angle BCF \cong \angle FED.. (alternate \: \angle 's) \\
\therefore \triangle CBF \cong \triangle EDF.. (By \: ASA\: Postulate) [/tex]
Answer: see proof below
Step-by-step explanation:
Statement Reason
1. CB || ED 1. Given
2. ∠E ≅ ∠C 2. Alternate Interior Angle Postulate
3. ∠D ≅ ∠B 3. Alternate Interior Angle Postulate
4. CB ≅ ED 4. Given
5. ΔCBF ≅ ΔEDF 5. ASA Congruency Theorem