which characteristics will prove that triangle def is a right, scalene triangle?
a. de, ef, and df are all different lengths, and their slopes are the same.
b. de, ef, and df are all different lengths, and the slopes of de and ef opposite reciprocals.

The correct option is B.

Step-by-step explanation:

Proprieties of a right angled triangle are

1. Sum of squares of two small sides is equal to the square of third side.

2. Two out of three sides are perpendicular.

The slope of two parallel lines are same.

In triangle DEF, the slopes of DE, EF, and DF are same it means the lines DE, EF, and DF are parallel. If three sides are parallel, then DEF can not be a triangle.

Therefore option A is incorrect.

The slope of two perpendicular lines are opposite reciprocals of each other because the product of slopes of two parallel sides is -1.

In triangle DEF, DE, EF, and DF are all different lengths, and the slopes of DE and EF opposite reciprocals. It means line DE and EF are parallel to each other or DEF is a right angled triangle.

Therefore option B is correct.