Diagonal $$BD$$ divides quadrilateral $$ABCD$$ into two triangles. Are these triangles congruent?
>(1) $$AD \parallel BC$$
>(2) $$AB=CD$$

Correct!
The issue here is whether quadrilateral $$ABCD$$ _must_ be divided into two congruent triangles by diagonal $$BD$$. By finding even one quadrilateral that cannot be divided into two congruent triangles, you have proved that both statements are insufficient.
If both statements are true, then the quadrilateral is either an isosceles trapezoid (a trapezoid whose legs are of equal length) or a parallelogram.
By definition, every parallelogram has congruent sides and therefore can be divided into 2 congruent triangles. However, an isosceles trapezoid meets conditions 1 and 2 but when divided by line $$BD$$, the resulting triangles are not congruent.

Incorrect.
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Incorrect.
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Incorrect.
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Incorrect.
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Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.

BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.