Question

which statement is false? a parallelogram
has diagonals that are perpendicular
has 2 sets of parallel sides
has diagonals that bisect each other (approximate text from image)

Explanation:

Step1: Recall properties of parallelograms

A parallelogram has 2 pairs of parallel sides (this is a defining property). The diagonals of a parallelogram bisect each other, but they are not perpendicular unless it's a rhombus (a special type of parallelogram). Also, the diagonals of a general parallelogram do not bisect each other at right angles (i.e., are not perpendicular) in most cases, and the statement "has diagonals that bisect each other" is true for parallelograms, but the green option says "has diagonals that are perpendicular" which is false for a general parallelogram (only true for rhombus, square etc., which are special parallelograms). Wait, wait, let's re - examine the options:

Wait, the options are:

Green: "Has diagonals that are perpendicular"

Blue: "Has 2 sets of parallel sides" (this is true for parallelogram)

Orange: "Has diagonals that bisect each other" (this is true for parallelogram)

So we need to find which statement is false. A general parallelogram does not have perpendicular diagonals (only rhombus, square, etc. do). So the green option's statement is false.

Answer:

Green option: "Has diagonals that are perpendicular"