Fox is working to prove the Base Angles Theorem. His proof is shown below. Critique his reasoning. Which statement or reason in his proof has a mistake? How can he fix his mistake? Given: Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ Prove: ∠B≅∠C Statements Reasons 1. Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ 1. Given 2. D , the midpoint of BC¯¯¯¯¯¯¯¯ AD¯¯¯¯¯¯¯¯ through points A and D 2. Construction 3. BD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ 3. Definition of midpoint 4. AD¯¯¯¯¯¯¯¯≅AD¯¯¯¯¯¯¯¯ 4. Reflexive property of congruence 5. △ABD≅△ACD 5. SAS Congruence Theorem 6. ∠B≅∠C 6. CPCTC Theorem(1 point) Responses Reason 3 has a mistake. It should say “Definition of angle bisector.” Reason 3 has a mistake. It should say “Definition of angle bisector.” Statement 6 has a mistake. It should say “∠A≅∠C." Statement 6 has a mistake. It should say “ angle upper A congruent to angle upper C ." Statement 3 has a mistake. It should say “∠BAD≅∠CAD." Statement 3 has a mistake. It should say “ angle upper B upper A upper D congruent to angle upper C upper A upper D ." Reason 5 has a mistake. It should say “SSS Congruence Theorem.”
Reason 3 has a mistake. It should say "Definition of midpoint."
Reason 6 has a mistake. It should say "CPCTC Theorem."
Statement 6 has a mistake. It should say "∠A≅∠C."
Statement 3 has a mistake. It should say "∠BAD≅∠CAD."
Reason 5 has a mistake. It should say "SAS Congruence Theorem."
To fix these mistakes, the correct proof would be:
1. Isosceles △ABC with AB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ (Given)
2. D, the midpoint of BC¯¯¯¯¯¯¯¯ (Construction)
3. BD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ (Definition of midpoint)
4. AD¯¯¯¯¯¯¯¯≅AD¯¯¯¯¯¯¯¯ (Reflexive property of congruence)
5. ∠BAD≅∠CAD (Definition of angle bisector)
6. △ABD≅△ACD (SAS Congruence Theorem)
7. ∠B≅∠C (CPCTC Theorem)