dissect the shapes into two congruent pieces

with one, connected line that goes dot to dot

fairly easy when one (half) shape is translated to the other:

involving a rotation of 180 degrees:

two identical halfs:

this time one of the halfs is rotated through 90 degrees to the other half

two similar shapes

one of the parts is an enlargement of the other (not scale factor 1)

powerpoints:

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