ABCD-parallelogram, M and N – midpoints of BC and AD sides. Prove that a quadrilateral is an AMCN-parallelogram.
| September 6, 2021 | education
By condition, ABCD is a parallelogram, therefore AD = BC, and they are parallel, which means that the MC and ND segments are also parallel, since they lie on these straight lines. Points M and N are the middle of the segments, therefore BM = MC, a AN = ND, and since BC = AD, then MC = AN.
Thus, the segments MC and AN are equal and parallel.
If in a quadrilateral two sides are equal and parallel, then this quadrilateral is a parallelogram.
Q.E.D.
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