Vertical angles are angles which are <u>opposite</u> to each other and have <u>equal</u> measures. With respect to the given proof, <em>Angie</em> completed the proof <em>incorrectly</em>.
<em>Two</em> angles are said to be <u>vertical</u> when they are <em>opposite</em> to one another and have <em>equal</em> measures. However, two angles are <u>supplementary</u> if they <u>add</u> <u>up</u> to 180°.
So, comparing Angie's and Becky's proofs, it can be deduced that from Angies proof:
1. Segment GH intersects segment AB at K (1. Given)
2. m∠AKG + m∠GKB = 180° (2. Definition of Supplementary Angles)
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)
Note:
- Step 2 should be Angle Addition Postulate, since:
m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
So that;
m∠AKG + m∠GKB = m∠GKB + m∠HKB
<u>Subtract</u> m∠GKB from both sides to have;
m∠AKG = m∠HKB (which is the proof for step 4)
Therefore, <u>Angie</u> completed the poof <em>incorrectly</em> because of the properties of steps 2 and 4.
A diagram is herewith attached for more clarifications.
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