Figure 5-60.-Bisecting a line by visual comparison.Dividing Lines and Areas EquallyYour ability to divide lines and areas into equalparts is necessary in arriving at many of thecommon geometric forms required in sketching.The simplest method of bisecting lines is by visualcomparison, as shown in figure 5-60. The entireline is first observed and weighed optically todetermine its fulcrum or point of balance. Eachhalf is compared visually before the bisectingpoint is placed. This procedure can be repeatedany number of times to divide a line into anynumber of equal divisions, merely by dividing andredividing its line segments.Centers of rectangular areas are easilydetermined by drawing their diagonals. Ifnecessary the halves can be divided with diagonalsfor smaller divisions, as shown in figure 5-61.Figure 5-61.-Locating centers by sketching diagonals.Figure 5-62.-Sketching angles by visual comparison.Sketching AnglesThe 90-degree angle is predominant in themajority of your sketches. Thus it is importantthat you learn to sketch right angles accurately,even if it entails checking them with the triangleoccasionally. Frequently, the perpendicular edgesof your paper can serve as a visual guide forcomparison. It is also helpful to turn your sketchupside down; non-perpendicular tendencies ofhorizontal and vertical lines will become evident.Shaping right angles correctly will give your sketchstability, without which effectiveness is lost.A 45-degree angle is made by dividing a rightangle by visual comparison; and a 30-degree or60-degree angle, by dividing the right angle intothree equal parts. The 30-degree or 45-degreeangle may be divided into equal parts in the samemanner. (See fig. 5-62.) Always start with the rightangle for the most accurate estimation of angleshape.Sketching Circles and ArcsPerfectly round circles are the most difficultto draw freehand. Figure 5-63 shows methods ofFigure 5-63.-Methods of sketching circles.5-31
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