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ltorline123
13.10.2019 •
Mathematics
Which is the most logical order of statements and justifications i, ii, iii, and iv to complete the proof?
a iii, iv, ii, i
b iv, iii, i, ii
c iii, iv, i, ii
d iv, iii, ii, i
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Ответ:
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![AG\cong GH](/tpl/images/0316/9632/e6668.png)
Justification: By construction
Step:IV![FG\parallel BH,GE\parallel CH](/tpl/images/0316/9632/1a4ce.png)
Justification: Midpoint segment theorem
Step III.![GC\parallel BH,BG\parallel CH](/tpl/images/0316/9632/5f2b0.png)
Justification: Substitution
Step I.BGCH is parallelogram
Justification: By property of parallelogram (Opposite sides are parallel)
StepII:![BD\cong DC](/tpl/images/0316/9632/5cf35.png)
Justification: Property of parallelogram (diagonals of parallelogram bisect each other)
Statement: AD is median
Justification: Definition of median
IV,III,I,II
Ответ:
Uhm, huh? If you're asking to play among us then sure!