Question 601873: My daughter did not get this right on a test:
Test question: With a straightedge draw a quadrilateral with no sides congruent. Construct the midpoints of each side and connect them in order. Determine the kind of figure that is formed and explain why it is this figure.
Her answer: The figure formed was a rhombus. Since I was connecting the midpoints of a quadrilateral itself. When I connected the midsegments, I found that the lines on opposite sides were parallel. (Teacher writes - HOW?) Since a rhombus is basically a stretched out square, the midpoints of the original figure gave the new figure a point to stretch out to. It shows that it doesn't matter that the sides of the original figure aren't congruent because that doesn't mean none of the sides of the new figure won't be either.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the figure formed is a parallelogram (actually, a Varignon Parallelogram)
a diagonal of a quadrilateral divides the quadrilateral into two triangles.
___ in each of the triangles; connecting the midpoints of the sides (which are sides of the parallelogram)
generates a line parallel to the base (which is the diagonal of the parallelogram)
___ since the two triangles have the same base (the diagonal), the "midlines" are parallel
this is also true for the other diagonal; giving two pairs of opposite parallel sides (a parallelogram)
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