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.
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

Answer 1

Linear pair angles, which are angles that together form a straight line are

supplementary angles.

The one that completed the proof incorrectly is Becky.

Reasons:

The two column proof is presented as follows;

Statement ${}$                                                             Reason

1. Segment GH intersects segment AB at K ${}$     1. Given

2. m∠AKG + m∠HKB = 180°    ${}$            2.Definition of Supplementary Angles

m∠GKB + m∠HKB = 180°

3. m∠AKG + m∠HKB = m∠GKB + m∠HKB      ${}$  3. Substitution property

4. m∠AKG = m∠HKB     ${}$                                      4. Subtraction Property

The difference between Angie's Proof and Becky's Proof is in Statement 2.

• Angie states that; m∠AKG + m∠HKB = 180° and m∠GKB + m∠HKB = 180° by definition of Supplementary Angles

• Becky states that; m∠AKG + m∠HKB = 180° and m∠GKB + m∠HKB = 180° by Angle Addition Postulate

Becky's proof is incorrect because the measure of angles  m∠AKG and

m∠HKB and m∠GKB and m∠HKB are not given, therefore, the use of the

reason of Angle Addition Postulate in statement 2. is incorrect.

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