Question

70 points! Mhanifa please help I don’t want to get this wrong :( thanks! Random answers will be reported !!

Answer 1

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.