Question

which postulate or theorem, if any,could be used to prove the triangles congruent? if not enough information is given, write not enough information

Answer 1

The ways we can prove the triangles congruent:

SAS (side, angle, side)
ASA (angle, side, angle)
AAS (angle, angle, side) 
SSS (all sides equal)
RHS/HL (Right Angle-Hypotenuse-Side/Hypotenuse-legs)

In these cases:
A. <B = <E
<A = <D
AC=DF

AAS (angle, angle, side) could be used.

B. AB=ED
BC=EF
AC=DF

SSS (all sides equal) could be used.

C.<BEA=<CED (right opposite angles)

As there is only one pair of equal angles we can find,there is not enough information.

D.<B = <E
BC=CE
<ECD < ACE(right opposite angles)

ASA (angle, side, angle) could be used.

Hope it helps!