Learning Event 4:

IDENTIFY THE USE OF DIAGONALS

1. The diagonals of the square sides establish the centers of these sides.

Verticals erected through each center, divide the side into halves.

In

order to divide the squares into quarters, find the center of a vertical

side and draw lines from this point receding toward the vanishing points.

This establishes the centers of the vertical edges. Now draw a diagonal in

one of the quarters so established. This diagonal will cross the diagonal

of the large square. Finally erect a vertical through the point established

by the intersection of these two diagonals. As you can see, this process of

division can be carried on as far as necessary to establish the required

division points on a horizontal edge or within the square itself.

2. It is also possible by using diagonals to add to the sides of the cube

in multiples of 2, 4, 8, etc., as shown in Figure 2-14. First, the center

of the square side is found and a vertical and horizontal are drawn through

this center. The horizontal is extended beyond the side of the cube toward

the vanishing point and the horizontal edges of the side are also extended

toward this point, as shown in Figure 2-14.

Figure 2-14.

Using diagonals to multiply areas