Answer:
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:
In order for a triangle to be isosceles, two of the line segments must be congruent. (eliminates choices C and D)
If the slopes of the congruent segments are negative reciprocals of each other, the triangle is a right triangle, not an acute triangle. (eliminates choice B)
With choices B, C, D eliminated, we are left with choice A.
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However, <em>that necessary description is not sufficient</em> to constrain the triangle to be an acute triangle. In order for the triangle to be acute, the third side must be less than √2 times the length of either of the congruent sides.
The correct answer is "none of the above."
