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1.E is the midpoint of AB⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅ED⎯⎯⎯⎯⎯ (Def. of mdpt.)3.E is the midpoint of BC⎯⎯⎯⎯⎯. (Given)4.BE⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯ (Def. of mdpt.)5.∠AEC≅∠BED (Sym. ∠s Thm.)6.△ABE≅△DCE (SSS Steps 1, 5, 4)7.∠EBA≅∠ECD (CPCTC)8.AB⎯⎯⎯⎯⎯ ∥CD⎯⎯⎯⎯⎯⎯ (Conv. of Alt. Int. ∠s Thm.)

1.E is the midpoint of AD⎯⎯⎯⎯⎯. (Given)2.AE⎯⎯⎯⎯⎯≅ED⎯⎯⎯⎯⎯ (Def. of mdpt.)3.E is the midpoint of BC⎯⎯⎯⎯⎯. (Given)4.BE⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯ (Def. of mdpt.)5.∠AEB≅∠CED (Vert. ∠s Thm.)6.△ABE≅△DCE (SAS Steps 1, 5, 4)7.∠EAB≅∠EDC (CPCTC)8.AB⎯⎯⎯⎯⎯ ∥CD⎯⎯⎯⎯⎯⎯ (Conv. of Alt. Int. ∠s Thm.)

1.E is the midpoint of AB⎯⎯⎯⎯⎯. (Given)2.AB⎯⎯⎯⎯⎯≅ED⎯⎯⎯⎯⎯ (Def. of mdpt.)3.E is the midpoint of BC⎯⎯⎯⎯⎯. (Given)4.BE⎯⎯⎯⎯⎯≅CD⎯⎯⎯⎯⎯⎯ (Def. of mdpt.)5.∠AEB≅∠CED (Supp. ∠s Thm.)6.△ABE≅△DCE (SSS Steps 1, 5, 4)7.∠EAB≅∠ECD (CPCTC)8.AB⎯⎯⎯⎯⎯ ∥CD⎯⎯⎯⎯⎯⎯ (Conv. of Alt. Int. ∠s Thm.)