Question

An ironing board manufacturer designs a folding ironing board with two legs. Each leg runs diagonally under the board from one end of the board to the floor, crossing over the other leg in the middle. Both legs are the same length. The designer connects the endpoints of the legs to form a quadrilateral. Which specific quadrilaterals could be formed? Explain your answer.

Answer 1

The quadrilateral that can be formed is a parallelogram.

The reason for this is that the two legs of the ironing board, being of equal length and crossing over each other, create two pairs of congruent adjacent sides. In a quadrilateral, if opposite sides are parallel and congruent, it is a parallelogram. Since the two pairs of adjacent sides of the quadrilateral formed by the ironing board are parallel and congruent, it must be a parallelogram.