Question

Amanda and Stephen wrote the following proofs to prove that vertical angles are congruent. Who is correct? Line segment NT intersects line segment MR, forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. Amanda's Proof Statement Justification ∠1 + ∠4 = 180° Definition of Supplementary Angles ∠3 + ∠4 = 180° Definition of Supplementary Angles ∠1 + ∠4 = ∠3 + ∠4 Substitution Property of Equality ∠1 ≅ ∠3 Subtraction Property of Equality Stephen's Proof Statement Justification ∠1 + ∠2 = 180° Definition of Supplementary Angles ∠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.

Answer 1

Both Amanda and Stephen are correct. They both used the definition of supplementary angles and the substitution and subtraction properties of equality to prove that vertical angles are congruent. Amanda’s proof shows that angles 1 and 3 are congruent, while Stephen’s proof shows that angles 1 and 3 are congruent. So, the correct answer is: Both Amanda and Stephen are correct

Explanation:

Answer 2

Both Amanda and Stephen are correct in their proofs.

Amanda's proof uses the definition of supplementary angles to establish that ∠1 + ∠4 = 180° and ∠3 + ∠4 = 180°. By equating these two equations, she correctly concludes that ∠1 ≅ ∠3. This is a valid proof of the congruence of vertical angles.

Stephen's proof also starts with the definition of supplementary angles, establishing that ∠1 + ∠2 = 180° and ∠2 + ∠3 = 180°. By equating these two equations, he correctly concludes that ∠1 ≅ ∠3. This is also a valid proof of the congruence of vertical angles.

Both proofs follow logical steps and use appropriate properties of angles and equality. Therefore, both Amanda and Stephen are correct in proving that vertical angles are congruent.

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