Final answer:
The missing statement in step 4 using the Reflexive Property for proving that triangles AEC and BDC are similar is 'c) ∠eac ≅ ∠eac'. option c is the correct answer.
Step-by-step explanation:
The student is given that the lines ae and ec are perpendicular, as well as bd and dc. They have to prove that triangles △aec and △bdc are similar.
The definition of perpendicular lines tells us that ∠aec and ∠bdc are right angles, making them congruent based on the fact that all right angles are congruent. For step 4 of the proof, we need to use the Reflexive Property to identify a side or angle that is equal to itself within the two triangles.
Since ∠eac is an angle in both △aec and △bdc, the correct option in the final answer is 'c) ∠eac ≅ ∠eac'. With two pairs of congruent angles, the two triangles are similar by the AA similarity theorem.