during a ten day period kids were given $1 on the first day $2 on the second day, and so on finishing with $10 on the 10th day.
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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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Answer:
<h2>The length of the line segment VT is 13 units.</h2>Step-by-step explanation:
We know that SU and VT are chords. If the intersect at point R, we can define the following proportion
Where
Replacing all these expressions, we have
Solving for , we have
Now, notice that chord VT is form by the sum of RT and RV, so
Replacing the value of the variable
Therefore, the length of the line segment VT is 13 units.