Question

Select One

Consider the following proof of the Triangle Angle Sum Theorem. Which statement has a mistake? How should the mistake be fixed? Given: △ABC with DE←→∥AC¯¯¯¯¯¯¯¯ Prove: m∠A+m∠ABC+m∠C=180° Statements Reasons 1. △ABC with DE←→∥AC¯¯¯¯¯¯¯¯ 1. Given 2. ∠DBA≅∠B; ∠EBC≅∠C 2. DE←→∥AC¯¯¯¯¯¯¯¯ and alternate interior angles are congruent when lines are parallel 3. m∠DBA=m∠A; m∠EBC=m∠C 3. Definition of congruent angles 4. m∠DBA+m∠ABC+m∠EBC=180° 4. Definition of a straight angle 5. m∠A+m∠ABC+m∠C=180° 5. Substitution(1 point) Responses Statement 2 has a mistake. It should say ∠DBA≅∠A; ∠EBC≅∠C. Statement 2 has a mistake. It should say angle upper D upper B upper A congruent to angle upper A ; angle upper E upper B upper C congruent to angle upper C . Statement 2 has a mistake. It should say ∠DBA≅∠B; ∠EBC≅∠A. Statement 2 has a mistake. It should say angle upper D upper B upper A congruent to angle upper B ; angle upper E upper B upper C congruent to angle upper A . Statement 4 has a mistake. It should say m∠A+m∠ABC+m∠C=180°. Statement 4 has a mistake. It should say m angle upper A plus m angle upper A upper B upper C plus m angle upper C equals 180 degrees . Statement 4 has a mistake. It should say m∠DBA+m∠ABC+m∠ACB=180°.

Answer 1

The mistake is in **Statement 2**. It incorrectly states that ∠DBA ≅ ∠B and ∠EBC ≅ ∠C. The correct statement should indicate that ∠DBA is congruent to ∠A and ∠EBC is congruent to ∠C due to the properties of parallel lines and corresponding angles.

The corrected statement should be:

**Statement 2 should say ∠DBA≅∠A; ∠EBC≅∠C.**

So, the correct choice would be: "**Statement 2 has a mistake. It should say ∠DBA≅∠A; ∠EBC≅∠C.**"