In quadrilateral abcd, diagonals ac and bd bisect one another:
which statement is used to prove that quadrilateral abcd is a parallelogram?

angles abc and bcd are congruent
sides ab and bc are congruent
triangles bpa and dpc are congruent
triangles bpc and cdp are congruent

Hello there,

Your correct answer would NOT be A.) "Angles ABC and BCD are congruent." They are NOT congruent. ABC and BCD do not have in agreement and they are not in harmony.

Your Correct answer would NOT be B.) "Sides AB and BC are congruent" My reason is because they do not align together. 

Your correct answer would NOT be D.) "Triangles BPA and DPC are congruent." The reason is because BPC and CDP does not line up together.

This conclude's that YOUR CORRECT answer would be "Triangles BPA and DPC are congruent ". The reason I say this is because BPA and DPC clearly are opposite of each other and they both go in harmony and they both are in agreement. They are congruent. 

Your correct answer is "Triangles BPA and DPC are congruent "

There is a attachment to explain.

Hope this helps.

~Jurgen