Given an angle formed by two lines with a common vertex, this page shows how to construct another angle from it that has the same angle measure using a compass and straightedge or ruler. It works by creating two congruent triangles. A proof is shown below.

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

This construction works by creating two congruent triangles. The angle to be copied has the same measure in both triangles

The image below is the final drawing above with the red items added.

Argument | Reason | |
---|---|---|

1 | Line segments AK, PM are congruent | Both drawn with the same compass width. |

2 | Line segments AJ, PL are congruent | Both drawn with the same compass width. |

3 | Line segments JK, LM are congruent | Both drawn with the same compass width. |

4 | Triangles ∆AJK and ∆PLM are congruent | Three sides congruent (SSS). |

5 | Angles BAC, RPQ are congruent. | CPCTC. Corresponding parts of congruent triangles are congruent |

- Q.E.D

- 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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