Mathematics, 02.12.2020 01:00, tinasidell1972
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)
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