Question

amandas proof

statement	justification
∠3 + ∠4 = 180°	definition of supplementary angles
∠1 + ∠4 = ∠3 + ∠4	substitution property of equality
∠1 ≅ ∠3	subtraction property of equality

stephens proof

statement	justification
∠2 + ∠3 = 180°	definition of supplementary angles
∠1 + ∠2 = ∠2 + ∠3	substitution property of equality
∠1 ≅ ∠3	subtraction property of equality

stephen is correct, but amanda is not
amanda is correct, but stephen is not
both amanda and stephen are correct
neither amanda nor stephen is correct

Explanation:

Step1: Analyze Amanda's proof

Amanda starts with $\angle1+\angle4 = 180^{\circ}$ and $\angle3+\angle4=180^{\circ}$ by the definition of supplementary angles. Then uses substitution to get $\angle1+\angle4=\angle3 + \angle4$ and subtraction property to show $\angle1\cong\angle3$. Her steps are logical and correct.

Step2: Analyze Stephen's proof

Stephen starts with $\angle1+\angle2 = 180^{\circ}$ and $\angle2+\angle3 = 180^{\circ}$ by the definition of supplementary angles. Then uses substitution to get $\angle1+\angle2=\angle2+\angle3$ and subtraction property to show $\angle1\cong\angle3$. His steps are also logical and correct.

Answer:

C. Both Amanda and Stephen are correct