Which characteristics will prove that ? def is an isosceles triangle? segment de and segment ef are congruent to each other but not to segment df, and their slopes are not related. segment de and segment ef are congruent, and their slopes are opposite reciprocals. segment de is larger than segment ef, and their slopes are not related. segment de is larger than segment ef, and their slopes are opposite reciprocals.

Option A: Segment DE and segment EF are congruent to each other but not to segment DF, and their slopes are not related.

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which 2 of the 3 sides are of exactly the same length. All isosceles triangles should have at least 2 sides to be equal. In the given triangle DEF, the sides include DE, DF, and EF. As mentioned, two of the sides out of three should be same. So 3rd and 4th options can be safely rules out. It is also important to note that the fact that two sides should be equal does not depend on the slopes of the lines. The angles can be of any size. That is, the triangle to be isosceles does not depend on the angles or the slopes of the lines. This means option B is also incorrect. So the correct choice is Option A!!!