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See also the animated version.

After doing this | Your work should look like this | |
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Start with a line segment PQ that we will copy. | ||

Step 1 | Mark a point R that will be one endpoint of the new line segment. | |

Step 2 | Set the compasses' point on the point P of the line segment to be copied. | |

Step 3 | Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ. | |

Step 4 | Without changing the compasses' width, place the compasses' point on the the point R on the line you drew in step 1 | |

Step 5 | Without changing the compasses' width, Draw an arc roughly where the other endpoint will be. | |

Step 6 | Pick a point S on the arc that will be the other endpoint of the new line segment. | |

Step 7 | Draw a line from R to S. | |

Step 8 | Done. The line segment RS is equal in length (congruent to) the line segment PQ. |

- Introduction to constructions
- Copy a line segment
- Sum of n line segments
- Difference of two line segments
- Perpendicular bisector of a line segment
- Perpendicular at a point on a line
- 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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All rights reserved