Answer:
A: Vertical angles are congruent, C is the midpoint of BE, and ∠B ≅ ∠E.
B: C is the midpoint of AD, BC ≅ EC, and Vertical angles are congruent.
C: I assume you cannot use CPCTC so AAS and ASA.
Explanation:
A: Since vertical angles are congruent, the interior angles using point C of the triangles are congruent. If C is the midpoint of BE, BC ≅ EC. Draw the congruent parts based on the 3 statements with tick marks and you will see that you have two pairs of congruent angles with an included pair of congruent sides, so ASA applies.
B: If C is the midpoint of AD, AC ≅ DC. Since vertical angles are congruent, the interior angles using point C of the triangles are congruent. Draw the congruent parts based on the 3 statements with tick marks and you will see that you have two pairs of congruent sides with an included pair of congruent angles, so SAS applies.
C: ∠B ≅∠E and ∠A ≅∠D since these are pairs of alternate interior angles. Since vertical angles are congruent, the interior angles using point C of the triangles are congruent and it is given that AB ≅ DE. When making the appropriate marks, you will see that only AAS and ASA can be used without CPCTC.