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After doing this | Your work should look like this | |
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Start with a line segment AB that we will divide up into 5 (in this case) equal parts. | ||

Step 1 | From point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important. | |

Step 2 | Set the compasses on A, and set its width to a bit less than one fifth of the length of the new line. | |

Step 3 | Step the compasses along the line, marking off 5 arcs. Label the last one C. | |

Step 4 | With the compasses' width set to CB, draw an arc from A just below it. | |

Step 5 | With the compasses' width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D. | |

Step 6 | Draw a line from D to B. | |

Step 7 | Using the same compasses' width as used to step along AC, step the compasses from D along DB making 4 new arcs across the line | |

Step 8 | Draw lines between the corresponding points along AC and DB. | |

Step 9 | Done. The lines divide the given line segment AB in to 5 congruent parts. |

- Introduction to constructions
- Copy a line segment
- Sum of n line segments
- Difference of two line segments
- Perpendicular bisector of a line segment
- Perpendicular from a line at a point
- Perpendicular from a line through a point
- Perpendicular from endpoint of a ray
- Divide a segment into n equal parts
- Parallel line through a point (angle copy)
- Parallel line through a point (rhombus)
- Parallel line through a point (translation)

- Bisecting an angle
- Copy an angle
- Construct a 30° angle
- Construct a 45° angle
- Construct a 60° angle
- Construct a 90° angle (right angle)
- Sum of n angles
- Difference of two angles
- Supplementary angle
- Complementary angle
- Constructing 75° 105° 120° 135° 150° angles and more

- Copy a triangle
- Isosceles triangle, given base and side
- Isosceles triangle, given base and altitude
- Isosceles triangle, given leg and apex angle
- Equilateral triangle
- 30-60-90 triangle, given the hypotenuse
- Triangle, given 3 sides (sss)
- Triangle, given one side and adjacent angles (asa)
- Triangle, given two angles and non-included side (aas)
- Triangle, given two sides and included angle (sas)
- Triangle medians
- Triangle midsegment
- Triangle altitude
- Triangle altitude (outside case)

- Right Triangle, given one leg and hypotenuse (HL)
- Right Triangle, given both legs (LL)
- Right Triangle, given hypotenuse and one angle (HA)
- Right Triangle, given one leg and one angle (LA)

- Finding the center of a circle
- Circle given 3 points
- Tangent at a point on the circle
- Tangents through an external point
- Tangents to two circles (external)
- Tangents to two circles (internal)
- Incircle of a triangle
- Focus points of a given ellipse
- Circumcircle of a triangle

- Square given one side
- Square inscribed in a circle
- Hexagon given one side
- Hexagon inscribed in a given circle
- Pentagon inscribed in a given circle

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