The method that cannot be used to prove ABC ~ ADE is (d) using the slope formula to show that the slopes of segments BC & DE are equal, and thus BC is parallel to DE and corresponding angles will be congruent by AA.
Of all the options, the first three options are valid options that can be used to determine if triangles ABC and ADE are similar.
However, option (d) cannot be used.
This is so, because the slopes of sides BC and DE does not guarantee that side lengths AB & AD, and AC and AE would have the same slope.
If the other corresponding sides do not have the same slope, then the triangles are not similar.
Hence, the method that cannot be used to prove ABC ~ ADE is (d)
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