Question 368763: Prove that midpoints of a quadrilateral form a parallelogram.
Answer by acalgebra(30)   (Show Source):
You can put this solution on YOUR website! The type of quadrilateral that is formed can either be a rhombus, a
rectangle, or a square, but it will always be a parallelogram. This is
because when the midpoints are connected to form the sides of the
midpoint-verticed figure, each side of the original figure is bisected. Each newly
formed side will be parallel to a diagonal of the original. Two of the
newly formed sides are parallel to the same diagonal and therefore are
parallel to each other. Along with the other two sides of the midpoint-verticed
that are parallel to the other diagonal of the original, a parallelogram
is formed.
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