Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?
2 answers:
Answer:
IV,III,I,II
Step-by-step explanation:
We are given that a triangle ABC in which three medians are given .
We are given a proof of three medians of a triangle which intersect at common point.
We have to find which is the most logical order of statement and justifications I,II,III and IV to complete the proof.
Statement:Point F is the mid- point of segment AB and point E is the mid-point of segment AC.
Draw segment BE and draw segment FC.
Justification: By construction
Statement: Point G is the point of intersection of segment BC and segment FC.
Justification: Intersecting lines postulate
Statement:Draw segment AG.
Justification: By construction
Statement:Point D is the mid- point of intersection between segment AG and segment BC.
Justification: Intersecting lines postulate
Statement:Point H lies on segment AG such that
Justification: By construction
Step:IV
Justification: Midpoint segment theorem
Step III.
Justification: Substitution
Step I.BGCH is parallelogram
Justification: By property of parallelogram (Opposite sides are parallel)
StepII:
Justification: Property of parallelogram (diagonals of parallelogram bisect each other)
Statement: AD is median
Justification: Definition of median
Answer:IV,III,I,II
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OK. All the work is in the attached drawing.
Please spend enough time with it to understand what was done and how, so that you can do the next problem like this one completely on your own.
Good luck !
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Here's a picky pickypoint to think about concerning the "cost". I'm not quite sure what to do about this:
The initial, one-time $55 is a "deposit". If she doesn't smash the bike or steal it, she gets the $55 back when she returns the bike.
So if she eventually gets the $55 back, <u><em>is it a cost</em></u> ? ? I don't know how to think about it.
She does need to <em>give</em> them the $55 at the beginning, just to take the bike out. So she has to have it with her and give it to them temporarily, even though she'll get it back, and she'll still have it when she returns home.
So here's the story:
-- While she HAS the bike, the graph correctly shows all the money she needs, in order to get the bike, and keep it for however long she keeps it.
-- Finally, at the end of the week, after she returns the bike and gets her $55 back, the line and everything on the graph will shift down by $55. The line will start at zero, and the little red ordered pairs will also shift straight down and still be on the line.
To put it one more way:
-- While Jen has the bike, the y-intercept of the graph is $55.
-- After she returns the bike in good condition, the y-intercept is zero.
