Adam wants to prove the Base Angles Theorem. On which statement or reason did he make a mistake? Also, how can fix his mistake?

Question

Given: Isosceles ∆ABC with AB ≅ AC
Prove: ∠B ≅ ∠C

Statements

1. Isosceles ∆ABC with AB ≅ AC
2. D, midpoint of BC, AD through points A and D
3. BD ≅ DC
4. AD ≅ AD
5. ∆ABD ≅ ∆ACD
6. ∠B ≅ ∠C

Reasons
1. Given
2. Construction
3. Definition of midpoint
4. Reflexive property of congruence
5. SAS Congruence Theorem
6. CPCTC Theorem

CHOOSE ONE ANSWER ONLY
a. Statement 3 has a mistake. It should say ∠BAD ≅ ∠CAD
b. Reason 3 is incorrect. It should say "Definition of angle bisector."
c. Statement 6 is incorrect. It should say "∠A ≅ ∠C."
d. Reason 5 is incorrect. It should say "SSS Congruence Theorem"

Answer 1

The correct answer is:

a. Statement 3 has a mistake. It should say ∠BAD ≅ ∠CAD.

In this construction, the midpoint of segment BC does not directly lead to BD ≅ DC affecting the angles at A as stated. Instead, the focus should be on showing that the angles at A (∠BAD and ∠CAD) are congruent due to the properties of isosceles triangles, which directly supports the proof of the Base Angles Theorem. To fix the mistake, the statement should indicate that ∠BAD ≅ ∠CAD rather than discussing the equality of the segments BD and DC.