match the proof. I need help please​

Accepted Solution

Answer:D, E, F, B, C, A, GStep-by-step explanation:D is the midpoint of AB, E is the midpoint of BC and DB || FCThis is given information from the diagram and statement.∠B ≅ ∠FCESince DB and FC are parallel, ∠B and ∠FCE are alternate interior angles, and therefore congruent.∠BED ≅ ∠CEF∠BED and ∠CEF are vertical angles, and therefore congruent.ΔBED ≅ ΔCEFBy angle-side-angle, these triangles are congruent.DE ≅ FE, DB ≅ FCCorresponding parts of congruent triangles are congruent.AD ≅ DB, DB ≅ FC, therefore AD ≅ FCFrom transitive property of congruence.ADFC is a parallelogramSince AD and FC are congruent and parallel, ADFC is a parallelogram.DE is parallel to ACSince ADFC is a parallelogram, DE is parallel to AC by definition of a parallelogram.