Given that E is the midpoint of AD¯¯¯¯¯ and BC¯¯¯¯¯, which of the following proves that ∠EAB≅∠EDC? The figure shows two triangles A B E and D C E with a common vertex E. Points A, E, D lie on one line. Points B, E, C lie on one line.

Answers are one of the following

a
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)

b
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)

c
1. E is the midpoint of AD¯¯¯¯¯. (Given)2. AB¯¯¯¯¯≅ED¯¯¯¯¯ (Def. of mdpt.)3. E is the midpoint of BC¯¯¯¯¯. (Given)4. BE¯¯¯¯¯≅CD¯¯¯¯¯ (Def. of mdpt.)5. ∠AEC≅ ∠BED (Vert. ∠s Thm.)6. △ABE≅ △DCE (SAS Steps 1, 5, 4)7. ∠EBA≅ ∠EDC (CPCTC)

d
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)