3.1 GEOMETRIC CONSTRUCTION

The following figures show the methods used to perform most of the basic geometric constructions used in standard drawing and layout practices. Many of these constructions have widespread use in the machine shop, the sheet metal shop, and in engineering.

• To divide any straight line into any number of equal spaces (Fig. 3.1). To divide line AB into five equal spaces, draw line AC at any convenient angle such as angle BAC. With a divider or compass, mark off five equal spaces along line AC with a divider or compass. Now connect point 5 on line AC with the endpoint of line AB. Draw line CB, and parallel transfer the other points along line AC to intersect line AB, thus dividing it into five equal spaces.

Figure 3.1: Dividing a line equally.

• To bisect any angle BAC (Fig. 3.2), swing an arc from point A through points d and e. Swing an arc from point d and another equal arc from point e. The intersection of these two arcs will be at point f. Draw a line from point A to point f, forming the bisector line AD.

Figure 3.2: Bisecting an angle.

• To divide any line into two equal parts and erect a perpendicular (Fig. 3.3), draw an arc from point A that is more than half the length of...