Chapter 5.2, Problem 7WE

To determine

To find: the theorem that the board is parallel to the floor $\left(\overline{AR}\parallel \overline{BD}\right)$ .

Answer to Problem 7WE

This further implies that $AR\parallel BD$

Therefore, it is proved that the board is parallel to the floor.

Explanation of Solution

Given information:

Given figure,

Given:

The legs of this ironing board are built so that $BO=AO=RO=DO$ .

Calculation:

In a quadrilateral $ABDR$ , note that

  $BO=AO=RO=DO$

From above equation, it can be conclude that

  $\begin{array}{l}AO=DO\mathrm{.............}(1)\\ BO=RO\mathrm{..............}(2)\end{array}$

From equation (1) and (2), the diagonal bisect each other at point $O$ .

If the diagonal bisect each other in a quadrilateral then the quadrilateral is a parallelogram.

This implies that $ABDR$ is a parallelogram, and then the opposite sides are parallel.

This further implies that $AR\parallel BD$

Therefore, it is proved that the board is parallel to the floor.