Given that in Isosceles △ABC, base BC¯¯¯¯¯, BE¯¯¯¯¯⊥AC¯¯¯¯¯, and CF¯¯¯¯¯⊥AB¯¯¯¯¯, which of the following proves that BE¯¯¯¯¯≅CF¯¯¯¯¯? The figure shows triangle A B C with segments C F and B E.

1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)2. AB¯¯¯¯¯≅AC¯¯¯¯¯ (Def. of Isosc. △)3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)4. m∠BEA=m∠CFA=90∘ (Def. of ⊥)5. ∠BEA≅∠CFA (Rt. ∠s ≅ Thm.)6. ∠A≅∠A (Reflex. Prop. of≅)7. △ABE≅△ACF (AAS Steps 5, 6, 1)8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)

1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)2. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Def. of Isosc. △)3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)4. ∠BEC and ∠CFB are Supplementary Angles (Def. of ⊥)5. AC¯¯¯¯¯≅BC¯¯¯¯¯ (Supp. ∠s ≅ Thm.)6. ∠A≅∠B (Sym. Prop. of≅)7. △ABE≅△ACF (SAS Steps 1, 6, 5)8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)

1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)2. AB¯¯¯¯¯≅AC¯¯¯¯¯ (Def. of Isosc. △)3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)4. m∠BEC=m∠CFB=90∘ (Def. of ⊥)5. ∠BEC≅∠CFB (Rt. ∠s ≅ Thm.)6. ∠A≅∠B (Sym. Prop. of≅)7. △ABE≅△ACF (AAS Steps 5, 6, 1)8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)

1. Isosc. △ABC, base BC¯¯¯¯¯ (Given)2. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Def. of Isosc. △)3. BE¯¯¯¯¯⊥AC¯¯¯¯¯, CF¯¯¯¯¯⊥AB¯¯¯¯¯ (Given)4. ∠BEA and ∠CFA are Supplementary Angles (Def. of ⊥)5. AB¯¯¯¯¯≅BC¯¯¯¯¯ (Supp. ∠s ≅ Thm.)6. ∠A≅∠A (Reflex. Prop. of≅)7. △ABE≅△ACF (SAS Steps 1, 6, 5)8. BE¯¯¯¯¯≅CF¯¯¯¯¯ (CPCTC)