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slega [8]
3 years ago
5

Given: ΔABC Prove: The three medians of ΔABC intersect at a common point.

Mathematics
1 answer:
Marta_Voda [28]3 years ago
7 0
<span>Given: ΔABC

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point are as follows:

Statements                                                          Justifications

Point F is a midpoint of Line segment AB        </span><span>by Construction               
Point E is a midpoint of Line segment AC
Draw Line segment BE
Draw Line segment FC 

Point G is the point of intersection between
Line segment BE and Line segment FC               Intersecting Lines Postulate

Draw Line segment AG                                        by Construction

Point D is the point of intersection between
Line segment AG and Line segment BC              Intersecting Lines Postulate

Point H lies on Line segment AG such that
Line segment AG ≅ Line segment GH                 by Construction

</span><span>Line segment FG is parallel to line segment
BH and Line segment GE is parallel to line
segment HC                                                         Midsegment Theorem

</span><span><span>Line segment GC is parallel to line segment
BH and Line segment BG is parallel to
line segment HC                                                  Substitution</span>

</span>BGCH is a                                                        <span><span><span><span>Properties of a Parallelogram </span>parallelogram                                                   (opposite sides are parallel)</span>

</span>Line segment BD ≅ Line segment                    </span><span><span>Properties of a Parallelogram </span>DC                                                                    (diagonals bisect each other)   

Line segment AD is a median                          Definition of a Median</span>

Thus the most logical order of statements and justifications is: II, III, IV, I
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