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7 June, 10:36

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.?

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  1. 7 June, 11:41
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    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.
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