# Which characteristics will prove that def is a right, isosceles triangle

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.

the slopes of DE and EF are opposite reciprocals make the triangle Δ DEF a right triangle.

Step-by-step explanation:

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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