Because CB=AC, BD=CE, angle C= angle C=90 degrees.

So in the triangle ZCDRT (congruent) triangle CEB,

So CD=CE

Because BC=AC

So AD=BE

So CD/AD=CE/BE.

DE//AB

So angle DEM= angle EBM= angle DAM= angle MDE.

So angle DEM= angle MDE

Triangle DEM is an isosceles triangle.