Instruction: Construct points that divide the segment into three equal parts using only a straightedge. To help you, a line parallel to the segment is given.
Goal: 8L 8E
Available Tools:
- Move
- Point
- Line
- Intersect
Pack: Kappa
Previous Level: 10.6
Next Level: 10.8
8L 8E Solution[]
Given the segment AB.
- Construct a line connecting A with an arbitrary point C on the line.
- Construct a line connecting B with another arbitrary point D on the line that intersects AC at E.
- Construct line AD.
- Construct line BC, intersecting AD at F.
- Construct line EF, intersecting CD at G.
- Construct line AG, intersecting BD at H.
- Construct line FH, intersecting AB at I and CD at J.
- Construct line EJ, intersecting AB at K.
- Point at I.
- Point at K.