Given that E is the midpoint of AD¯¯¯¯¯ and BC¯¯¯¯¯, which of the following proves that ∠EAB≅∠EDC? 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. 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)

D.)

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)