In the rhombus ABCD, the diagonals intersect at point O. a) determine the type of BMDN

In the rhombus ABCD, the diagonals intersect at point O. a) determine the type of BMDN quadrilateral b) indicate pairs of equal triangles.

The diagonals of the rhombus are divided in half at the intersection point, then BO = DO. Since, by condition, BO = ОМ = ОN, then DO = BO = ОМ = ON. Then MN = BD.

The diagonals of the rhombus at the intersection point form a right angle, then in the MBND quadrangle the diagonals are equal and intersect at right angles and are divided in half, therefore, the quadrilateral is a square.

Pairs of equal triangles: Triangle ABM = ANC = DAM = DCN, triangle PTO = BON = DON = DOM, triangle ABN = ADN = CBM = CDM.