In rhombus ABCD, the diagonals meet at point O. On the AC diagonal there are segments ОМ and ОN equal to

In rhombus ABCD, the diagonals meet at point O. On the AC diagonal there are segments ОМ and ОN equal to BO a) determine the type of BMDN quadrilateral b) Specify pairs of equal triangles

The solution of the problem:
A rhombus is a quadrangle in which all sides are equal, opposite angles are equal. The diagonals of the rhombus are perpendicular, that is, when they intersect, four right angles are formed. At the point of intersection, the diagonals are halved. a) Consider the BMDN quadrangle. The sides of this quadrangle are equal, since they lie opposite equal angles. The diagonals are also equal, since ОМ = ОN = ОВ = ОD. The resulting quadrilateral BMDN is a square.
b) Triangle ABD is equal to triangle BCD, ABC is equal to ADC, OBC is equal to ODC, since these triangles have two sides and the angle between them.