Answer:
Congruent pairs of triangles:
ΔABD ≅ ΔDCB
- AB≅CD - given
- ∠ABD ≅ ∠CDB - given
- BD≅DB - common side
- SAS - two sides and the included angle
ΔABD ≅ ΔEFD - SAS
- AB≅EF - given
- ∠ABD ≅ ∠EFD - given
- ∠ADB ≅ ∠EDF - vertical angles
- AAS - two angles and non-included side
By using the above two we can state that:
ΔBDC ≅ ΔDFE - by ASA or SSS
because
- BD ≅ DF (corresponding parts)
- AD ≅ BC (corresponding parts)
- AD ≅ ED (corresponding parts)
- and therefore BC ≅ ED
We can't prove that:
- ΔAGD is congruent with any of the others as not enough information
There is one side and one angle and we can' t get two angles or two sides with included angle. Maximum we can get is SSA which doesn't guarantee the congruence.