<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
Answer:
x = 19
Step-by-step explanation:
Solve for x:
3 x + 43 = 100
Subtract 43 from both sides:
3 x + (43 - 43) = 100 - 43
43 - 43 = 0:
3 x = 100 - 43
100 - 43 = 57:
3 x = 57
Divide both sides of 3 x = 57 by 3:
(3 x)/3 = 57/3
3/3 = 1:
x = 57/3
The gcd of 57 and 3 is 3, so 57/3 = (3×19)/(3×1) = 3/3×19 = 19:
Answer: x = 19
You multiply all the numbers by 2 to get rid of the fractions. This would leave you with k + 1 = 6. Then you subtract 1 from both sides to get k = 5.
The answer is 6 since 2*6 is 12 and 12-8 is 4
