BG is the height of triangle ABC (when we use AC as our base), and EC is the height of triangle DEF (when we use DF as our base).
It's confusing to use all those capital letters, so let's use 'h' for the height BG, and 'j' for the height EC. We also have three important lengths along the horizontal base, AD, DC and CF, which I'll call 'a', 'b' and 'c' respectively.
Statement 1 then just tells us that h(a+b)/2 > j(b+c)/2, or multiplying by 2, that h(a+b) > j(b+c). Now maybe h > j, but maybe instead h < j, and a is really big and c is really small.
Statement 2 tells us that a = c, which is clearly not sufficient alone.
Combining the two statements, using a=c to substitute in our inequality from Statement 1, we have
h(a + b) > j(b + a)
and since a+b is positive, we can safely divide by a+b on both sides to get h > j, which is what we wanted to know. So the answer is C.
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