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Let a square ABCD in which L,M,N&O are the midpoints .

in triangle AML and triangle CNO AM = CN ( AB = DC and M and O are the midpoints ) AL = CM ( AD = BC and L and N are the midpoints ) angle MAL = angle NCO ( all angles of a square = 90 degree ) by AAS critaria triangle AML CONGRUENT to triangle CNO therefore ML = ON ( CPCT ) similarly in triangle MBN CONGRUENT to LDO and AND triangle AML is CONGRUENT to triangle now , in Triangle AML , angle AML = angle ALM ( AM = AL ) = 45 degree similarly in triangle LDO angle DLO = 45 degree there fore , angle MLO = 90 degree

by the properties of SQUARE all sides are equal and angles are 90 degree