Question 832299: Consider quadrilateral ABCD. If the midpoint of AB is E, the midpoint of BC is F, the midpoint of CD is G, the midpoint of AD is H. What conclusions can you make about quadrilateral EFGH? Justify.
EXPLORE for at least three different quadrilaterals of the following six: Quadrilateral with no special properties, parallelogram, rectangle, rhombus, square, trapezoid. Justifications can include measuring sides and angles
Frankie
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! Consider quadrilateral ABCD. If the midpoint of AB is E, the midpoint of BC is F, the midpoint of CD is G, the midpoint of AD is H. What conclusions can you make about quadrilateral EFGH? Justify.
EXPLORE for at least three different quadrilaterals of the following six: Quadrilateral with no special properties, parallelogram, rectangle, rhombus, square, trapezoid. Justifications can include measuring sides and angles
Frankie
Draw diagonals AC and BD
 
In the figure on the left:
HG is the midsegment of ΔDAC so HG∥AC
EF is the midsegment of ΔABC so EF∥AC
So EF∥AC, since lines parallel to the same line
are parallel to each other.
In the figure on the right:
EH is the midsegment of ΔABD so EH∥BD
FG is the midsegment of ΔDBC so FG∥BD
So EH∥FG, since lines parallel to the same line
are parallel to each other.
So EFGH is a parallelogram because both pairs of opposite sides are
parallel.
I'll finish this later.
Edwin
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