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 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 3 has a mistake. It should say “Definition of angle bisector.” Reason 3 has a mistake. It should say “Definition of angle bisector.” Reason 5 has a mistake. It should say “SSS Congruence Theorem.” Reason 5 has a mistake. It should say “SSS Congruence Theorem.” 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 ." Skip to navigation

Answer 1

Fox's proof contains mistakes that can be critiqued based on the statements and reasoning provided.

1. Critique of Statement 3: The statement "BD ≅ DC" is correct as it follows from the fact that D is the midpoint of BC. However, it’s important to note how this relates to the angles in the proof. The critique suggesting it should state angles instead of segments is misplaced; the statement is fine as it is because he lays down a segment relation.

2. Critique of Statement 5: The reason provided is the SAS (Side-Angle-Side) Congruence Theorem, which is incorrect here. While the statement is correct if we are considering lengths and angle properties, the correct theorem for the congruence of triangles ABD and ACD, given that we know two sides and the included angle are congruent, is actually SAS. Ancak referans verilirken açıların da benzer olduğunu gözden kaçırdığınızı belirtmelisiniz.

3. Critique of Statement 6: The statement ∠B≅∠C is actually correctly concluded based on the triangles being congruent. The reference to angles must be consistent throughout the proof, and CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is correctly applied here.

Mistake Summary & Fixes:

1. Statement 3 is acceptable; no fix is needed here.
2. Reason 5 should read "SAS Congruence Theorem" since the two sides and the included angle are used to establish congruence.
3. Statement 6 is fine as is; no fix is needed here.

Revised Proof Steps:

• Maintain Statement 3 as "BD ≅ DC" with no change.
• Confirm the triangles are proven congruent by using the correct SAS theorem in Statement 5.
• Confirm Statement 6 as it is.

Thus, the most critical point of confusion seems to arise in the description of triangle congruence rather than the conceptual understanding of triangle congruence or base angles theorem itself. Make sure to keep the terminology clear and consistent for all portions of the proof.

Answer 2

the one you just answered. the answers are: a: statement 3 has a mistake. it should say "/_BAD ~= /_ CAD"
B: reason 3 has a mistake. it should say "definition of angle bisector"
c: reason 5 has a mistake. is should say "sss congruence theorem."
and d: statement 6 has a mistake. it should say "/_a ~= '_c"

Answer 3

Thank you for your clarification. Let’s analyze the proof again in light of the provided correct answers.

1. Statement 3 mistake: The statement should indeed express an angle relationship but appears to wrongly refer to the segments. The correct expression would be “∠BAD ≅ ∠CAD.” This implies that the angle measures are being compared, focusing on the angles rather than the segments.

2. Reason 3 mistake: Referring to “Definition of angle bisector” implies that there is an angle bisector in play, which is not established in the proof. This could be a misunderstanding—since D is the midpoint of BC, it doesn’t imply the angles are anything other than equal through properties of isosceles triangles.

3. Reason 5 mistake: The suggestion that it should say "SSS Congruence Theorem" reflects a misunderstanding. In fact, since one angle is included between two sides that are known to be congruent (by sides AB and AC), the correct theorem for this situation is indeed SAS, not SSS.

4. Statement 6 mistake: A reference to angles in Statement 6 is appropriate, so it should correctly be stated as “∠A ≅ ∠C” or similar, as the concluding relationship involving the angles of the triangles.

Summary of Corrections:

• Statement 3: Corrected to “∠BAD ≅ ∠CAD.”
• Reason 3: Needs clarification but should avoid the angle bisector which is not part of the given proof.
• Reason 5: Should correctly reference "SAS Congruence Theorem."
• Statement 6: Should be stated as “∠A ≅ ∠C.”

Ultimately, the focus should emphasize that angles rather than segments or incorrect theorem references should be consistently applied to establish the proof regarding the base angle theorem correctly. If Fox intends to show that ∠B and ∠C are congruent, these points need precise articulation in line with the triangle properties being used.

Answer 4

so which answer should i use?

Answer 5

Based on your provided options for critiquing Fox's proof, here’s a breakdown of the responses and the correct interpretations:

1. Statement 3 has a mistake. It should say "∠BAD ≅ ∠CAD." - This response points out that Statement 3 incorrectly addresses segments instead of angles.

2. Reason 3 has a mistake. It should say "Definition of angle bisector." - This response is incorrect in the context of Fox's proof since it is based on the midpoint of segment BC, not an angle bisector.

3. Reason 5 has a mistake. It should say "SSS Congruence Theorem." - This is incorrect; the proof actually follows the SAS (Side-Angle-Side) Congruence Theorem due to your given two sides and the included angle.

4. Statement 6 has a mistake. It should say "∠A ≅ ∠C." - This statement incorrectly pertains to angles A and C when the proof is about angles B and C.

Conclusion

The best answer to select from your options is:

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

The critique of Statement 3 most accurately identifies an error in the original proof, which misrepresents the relationships involved regarding angles in the isosceles triangle. Thus, using this critique would be appropriate in expressing where Fox's argument lacks clarity or accuracy.

Answer 6

okay, thank youuuuuuuuu!! :D

Answer 7

You're very welcome! I'm glad I could help. If you have any more questions or need further assistance, feel free to ask. Good luck with your studies, and have a great day! :D