We are asked why the keyboard always remains parallel to the floor. Let's treat the legs of the keyboard as the diagonals of a quadrilateral.
We are given that the legs of the keyboard are joined at the midpoints. In other words, the diagonals of the quadrilateral bisect each other. Recall one of the Conditions for Parallelograms.
Condition for Parallelograms
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Our quadrilateral satisfies the Condition for Parallelograms. From the definition of a parallelogram, we know that a parallelogram is a quadrilateral that has two pairs of parallel opposite sides. As the keyboard and the floor are opposite sides of our parallelogram, they will always remain parallel to each other.
Extra
Conditions for Parallelograms
When trying to prove that a quadrilateral is a parallelogram, we should remember that there is more than one way to do it. Let's recall the Conditions for Parallelograms.
Conditions for Parallelograms
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.
