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.?

Becky made a mistake in statement (2)

Complete question:

Explain.

line AB intersecting line GH at K

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

Step-by-step explanation:

Correct Proof,

Statements Reasons

1). Segment GH intersects AB Given

at K.

2). m∠AKG + m∠GKB = 180°, Definition of supplementary

m∠GKB + m∠HKB = 180° angles

3). m∠AKG + m∠GKB = m∠GKB + m∠HKB Substitution property

4). m∠AKG = m∠HKB Subtraction property

By comparing this proof with the proves given we find Angie was correct.

Becky made a mistake in statement (2) by giving the reason of the statement as Angle addition postulate which should be Definition of supplementary angles.