# Connecting the midpoints of a quadrilateral's four sides forms a square. Must the original quadrilateral be a square?

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Connecting the midpoints of a quadrilateral's four sides forms a square. Must the original quadrilateral be a square?
posted Sep 24, 2018

+1 vote

Yes, it must.

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 daughter figure, each side of the mother figure is bisected. Each newly formed side will be parallel to a diagonal of the mother. 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 daughter that are parallel to the other diagonal of the mother, a parallelogram is formed.

answer Sep 24, 2018

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