last option
step-by-step explanation:
given that Ξ΄def is right and isoceles,
assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90Β° and are of equal length.
because they are of equal length, we can say that they are congruent
because they intersect at 90Β°, their slopes must be opposite reciprocals.
only the last option satisfies these conditions.