Question

Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who completed the proof incorrectly? Explain.
Angie's Proof

Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. m∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Definition of Supplementary Angles

3. m∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. m∠AKG = m∠HKB 4. Subtraction Property



Becky's Proof

Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. m∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Angle Addition Postulate

3. m∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. m∠AKG = m∠HKB 4. Subtraction Property

Answer 1

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