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.
the slopes of DE and EF are opposite reciprocals make the triangle Δ DEF a right triangle.
The characteristics will prove that Δ DEF is a right isosceles triangle is the lengths of DE and EF are congruent, and their slopes are opposite reciprocals.
Now, the equal sides of DE = EF make the triangle Δ DEF an isosceles triangle and the slopes of two perpendicular lines are always the opposite reciprocals.
So the correct answer would be: The lengths of DE and EF are congruent, and their slopes are opposite reciprocals.
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