last option
step-by-step explanation:
given that δdef is right and isoceles,
assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.
because they are of equal length, we can say that they are congruent
because they intersect at 90°, their slopes must be opposite reciprocals.
only the last option satisfies these conditions.
![Which characteristics will prove that def is a right,isosceles triangle](/tpl/images/05/02/CuwDWV9rHcmqRj0C.jpg)