Problem 174
The legs of an ironing board are equal in length and bisect each other at the point where they cross. What generalization about parallelograms ensures that the ironing board will always be parallel to the floor, regardless of the height of the board above the floor?
Solution
A parallelogram is characterized for having two diagonals that bisect each other. A parallelogram has two sets of parallel lines. If we see our ironing board as a parallelogram, then we can conclude that the board itself will be parallel to the opposite side, which is the floor. So, our ironing board, with the legs designed so that they cross and bisect each other, will have the top parallel to the floor.
What happens if the legs do not bisect each other. So then the turning point is not in the middle.
Also interesting, what happens if the legs are not equal in length?