Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete
d 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
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
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