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6 September, 00:24

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 Transitive 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 Transitive Property of Equality ∠1 ≅ ∠3 Subtraction Property of Equality

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  1. 6 September, 00:47
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    The answer:

    the valid proof is Amanda's.

    Statement Justification ∠1 + ∠4 = 180°

    Definition of Supplementary

    Angles ∠3 + ∠4 = 180°

    Definition of Supplementary Angles

    ∠1 + ∠4 = ∠3 + ∠4

    Transitive Property of Equality ∠1 ≅ ∠3
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