Question

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?

Answer 1

Look at the isoceles triangle at the top and at the bottom. The central angle is the same for each (opposite angles) and the legs are equal so the triangles are congruent. Therefore the angles where each leg meets the floor and the deck are congruent. Equal opposite interior angles ---> parallel.