∠A ≅ ∠A(reflective property of congruence)
Criteria for congruence of triangles.
∆ABE ≅ ∆ACD
D is the midpoint of AB (given)
E is the midpoint of AC(given)
∠B ≅ ∠C (corresponding parts of congruent triangles are congruent CPCTC)
∠DFB ≅ ∠EFC(vertical angles are equal)
AB ≅ AC(Corresponding parts of congruent triangles are congruent)
∠A ≅ ∠A(reflective property of congruence)
BC = 1/2AC( when midpoint divides a segment into two parts, each half is half the length of the whole segment)
BD ≅ EC(segments that are half the lengths of congruent segment are congruent)
∆DFB ≅ ∆EFC(AAS)
DF ≅ EF(Corresponding parts of congruent triangles are congruent).
The statement "∠A ≅ ∠A (reflexive property of congruence)" is a reflection of the reflexive property of congruence in geometry. The reflexive property states that any geometric figure or angle is congruent to itself.
Therefore,∠A ≅ ∠A(reflective property of congruence)