Solution:Step 1.Step 2.Using A as a center and a radius more than1/2 of AB, but less than AB, draw an arc.Using B as a center and the same radius asStep 1, draw an arc intersecting the arcdrawn in Step 1. Mark intersecting points Xand Y. Draw XY.Conclusion:AE = EBNOTE: That E also represents the midpoint of XYand that XY is perpendicular to AB. XY is termed theperpendicular bisector of AB,CONSTRUCTION OF PARALLELLINES USING PERPENDICULARSExample;Construct parallel lines 2“ apart.Solution:Step 1. Draw a base line and lay out two points Aand B 2" apart.Step 2. Construct perpendiculars AC and BD toAB at A and B.Conclusion;AC is parallel to BD.Principle:Perpendiculars to the same line are parallel.NOTE: Horizontal parallel lines can be drawn bythe same procedures.DIVIDING LINESLines can be divided into equal parts by a numberof methods. Four of these methods are (1) by usingparallel lines, (2) by transferring angles, (3) by usingequal segments on the side of an angle, and (4) by usinga scale.1. Using parallel linesExample;Divide AB into 5 equal parts.Solution:Step 1.Step 2.Step 3.Step 4.Assume any angle ABD and draw BD.At A construct Z BAC equal to Z ABD.Now BD and AC are parallel.Assume a radius so that 5 times the radiuswill fall within the BD, Swing arcs usingthis radius on BD and AC.Connect B with the last arc swung from Aand connect corresponding points.Conclusion:Lines drawn in Step 3 divide AB into 5 equal parts.2. Transferring anglesExample:Divide AB into 5 equal parts.AII-6