Which of the following conditions does not ensure that a quadrilateral is a parallelogram?
A) Both pairs of opposite sides are parallel.
B) The diagonals bisect each other.
C) A pair of opposite angles are congruent.
D) All of the above
Can anyone tell me if C is the right answer?
I agree with C because I can easily draw a four sided figure with a pair of opposite angles congruent and the other pair not congruent.
To determine which condition does not ensure that a quadrilateral is a parallelogram, we need to consider the properties of a parallelogram.
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. Additionally, the opposite angles of a parallelogram are congruent, and its diagonals bisect each other.
Now, let's evaluate each option:
A) Both pairs of opposite sides are parallel: This is a property of a parallelogram, so it matches the definition.
B) The diagonals bisect each other: This is another property of a parallelogram, so it also matches the definition.
C) A pair of opposite angles are congruent: This is yet another property of a parallelogram, so it matches the definition.
Since all of the given conditions (A, B, and C) are properties of a parallelogram, option (D) - "All of the above" - is the correct answer. None of the conditions given is incorrect or fails to ensure that the quadrilateral is a parallelogram. Therefore, option (C) is not the correct answer.