The quadrilateral abcd is a rhombus with diagonals ac =12 ft and bd = 4 ft. the points m and n divide diagonal ac on three equal parts. prove that bmdn is a square and find its area.

Let o be a point of rhombus's diagonals intersection. am=mn=nc=4 cm (from conditions data).ao=oc=6 cm, bo=od=2 cm (since diagonals of rhombus are is divided into equal parts by point o).let consider a quadrilateral bmdn. bd and mn are its diagonals. you have bo=od=2 cm and mo=on= 2cm (because mo=ao-am=6-4=2cm and on=co-no=6-4=2 cm). since diagonals are congruent and perpendicular and are divided into equal parts by intersection point o, the quadrilateral bmdn is square.

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