Is the quadrilateral ABCD a square?
(1) All four sides of ABCD have the same length.
(2) Two of the adjacent angles of ABCD add up to 180 degrees.
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.
(E) It is important that you're not fooled by questions like these. On the surface of statement (1), it would immediately seem that a quadrilateral with four sides of equal length would be a square. Remember, however, that this property also applies to a rhombus. Statement (1) is therefore insufficient. Statement (2) is also insufficient. All parallelograms have this property. Taken together, both statements are still insufficient. The quadrilateral could still be either a rhombus or a square. The answer is (E).
Hi, I don't understand statement 2:
In a parallelogram not any 2 of adjacent angles. If the inside angles of the parallelogram are 60 and 120, then you may add the two 60 degrees adjacent angles together. Can you please clarify this.