In the parallelogram ABCD on the sides BC and AD Are the points M and N respectively marked so that the line MN

| July 8, 2021 | education

In the parallelogram ABCD on the sides BC and AD Are the points M and N respectively marked so that the line MN passes through the intersection of the diagonals of the parallelogram? Prove that an AMCN -parallelogram quadrangle

Let us prove that triangle MOC is equal to triangle AON.

The segments OA and CO are equal as half the diagonals. The angle MOC is equal to the angle AON as vertical angles. The angle MCO is equal to the angle OAN as criss-crossing angles at the intersection of parallel straight lines ВС and АD of the secant AC. Then the triangles MOC and AON are equal in side and two adjacent angles, and then MC = AN.

Let us prove the equality of triangles AMC and ANC. The AC side of the triangles is common, and we proved that MC = AN, and the angle MCO = OAN, then the triangles are equal in two sides and the angle between them.

Then, in the quadrangle AMCN, the side CM = AN, the side AM = CD, and therefore the quadrilateral parallelogram along equal opposite sides, which was required to be proved.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.