What series of transformations to quadrilateral abcd map the quadrilateral onto quadrilateral efgh to prove that abcd≅efgh ? a reflection across x-axis, and then a translation 2 units up a reflection across y-axis, and then a translation 2 units down a reflection across y-axis , and then a translation 2 units up a reflection across x-axis, and then a translation 2 units down

For this case we have the following transformation rule:
 (x, y) > (x, - y - 2) > (x ', y')
 We are going to apply the following transformation rule for vertex D, for example.
 We have then:
 (4, 1) > (4, - 1 - 2) > (4, -3)
 Therefore, the transformation is:
 Reflection on the x axis and vertical displacement 2 units down.
 
 a reflection across x-axis, and then a translation 2 units down