Given below are two statements:
Statement (I): The diagonals of a parallelogram are always equal in length.
Statement (II): The diagonals of a parallelogram bisect each other.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Statement I is false but Statement II is true
Statement (I): The diagonals of a parallelogram are always equal in length. Incorrect. The diagonals are equal only when the parallelogram is a rectangle (or a square); in any other parallelogram, such as a rhombus that is not a square, one diagonal is longer than the other.
Statement (II): The diagonals of a parallelogram bisect each other. Correct. This holds for every parallelogram: the two triangles formed at the crossing point opposite each other are congruent, so each diagonal cuts the other into two equal halves.