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Using an Unmarked Ruler and Compass, Trisect a Line, four methods

How to Divide a Line into Three Equal Parts Using an Unmarked Ruler and Compass (Four Methods): Dividing a line into three equal parts can be achieved using an unmarked ruler and compass in four different ways. Let's break it down step by step—it's super simple! Trisect a Line, Method 1: 1. Draw any line segment AB. 2. Use point A as the center and AB as the radius to draw an arc. 3. Use point B as the center and AB as the radius to draw another arc. 4. Identify the intersection points C and D. 5. Draw a line through points A and C, intersecting arc A to obtain point E. 6. Draw a line through points B and E. 7. Draw a line through points A and D. 8. Identify the intersection point F. 9. Draw a line through points C and F, intersecting AB to obtain point G. 10. Use G as the center, AG as the radius, and draw arcs intersecting GB to obtain point H. 11. Confirm that AG = GH = HB. Trisect a Line, Method 2: 1. Draw any linesegment AB. 2. With A as thecenter, draw a circle with a radius smaller than AB. 3. Draw a diagonal linepassing through point A, intersecting at points C and D. 4. Draw a line passingthrough points C and B. 5. Use a compass tofind the perpendicular bisector of CB. 6. Locate the midpoint E of CB. 7. Draw a line passingthrough points D and E, intersecting line AB at point F. 8. With F as the centerand AF as the radius, draw points G where it intersects with FB. 9. Confirm that AF = FG= GB. Trisect a Line, Method 3: 1.Draw any line segment AB. 2.With A and B as centers, draw two circles with radii equal to AB. 3.With the intersection of the two circles as the center, draw a circle with a radius equal to AB. 4.Mark the intersection points as C and D. 5.Draw a line passing through points B and C, intersecting circle C at point E. 6.Draw a line passing through points E and D, intersecting AB at point F. 7.Use a compass with F as the center and AF as the radius to draw a circle intersecting AB at point G. 8.Now, AF = FG = GB. Trisect a Line, Method 4: 1. Draw any line segment AB. 2. With A and B as centers, draw arcs with radii equal to AB, intersecting at points C and D. 3. Draw a line through points B and D. 4. Draw a line through points A and C. 5. Use a compass to divide the line segments BD and AC into equal parts, obtaining points E, F, G, H such that AE = EF = GH = HB. 6. Draw lines through points H, F, and E, G. 7. On the line AB, mark points I and J. 8. Finally, you will have AI = IJ = JB. 9. Similarly, you can trisect the line segment at any desired points. Thanks for watching!