Question #bcaa7
1 Answer
Nov 13, 2016
The poligon inscripted in the midpoints of any quadrilateral is a parallelogram because each its side is proportional
to one of the two diagonals of the given quadrilateral
Explanation:
Once you have taken the mid points on each side of a quadrilateral ABCD, draw one of the two diagonals. If you consider the two segments joining the mid points of the sides emerging from the vertices opposite the drawn diagonal you can realize that these segments are parallel to it beacause they are bases of triangles similar in the ratio 1/2 and the angles at the base are equal. From this comes out that each segment of of the inscripted quadrilateral is parallel to one of the two diagonal of the given quadrilateral.
