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E, I screwed this one up. Not a silly mistake, just a knowledge gap.

The missing link for me was to see that the angles of the smaller triangle were similar to the larger triangle.
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By Applying Midpoint Theorem, we can determine with the help of Statement 1 alone that DE is parallel to BC.

Statement 2 is Insufficient to provide proof of triangle similarity.

Hence, Ans A

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A

From (1) AED is similar to ABC => angle ADE= angle ABC => DE is parallel to BC=> suff
From (2) There will be insufficient condition to ensure AED is similar to ABC => insuff
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Bunuel

how to prove that two lines are parallel? what should i look for ? interior angles to be supplementary?
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Bunuel

how to prove that two lines are parallel? what should i look for ? interior angles to be supplementary?

From (1) DE turns out to be a Midsegment of a Triangle (A line segment joining the midpoints of two sides of a triangle).

The midsegment is always parallel to the third side of the triangle.
• The midsegment is always half the length of the third side.
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