Which characteristics will prove that δdef 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.

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:

An isosceles triangle is a triangle whose two sides are equal out of three sides. In the above mentioned triangle ΔDEF, the sides are DE, DF and EF. An isosceles triangle should have at least two sides equal. According to this statement  3rd and 4th option are of no use. Now always remember that the fact that two sides must be equal does not involve the slopes of the line. Also the angle can be of any size. It means that an isosceles triangle does not depend on angle or the slopes of the line. This shows that option B is alose incorrect and Option A is correct statement