This page shows how to construct a triangle given one side and the angle at each end of it with compass and straightedge or ruler. It works by first copying the line segment to form one side of the triangle, then copy the two angles on to each end of it to complete the triangle. As noted below, there are four possible triangles that be drawn - they are all correct.

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.

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

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

1 | Line segment JL is congruent to AB. | Drawn with the same compass width. For proof see Copying a line segment |

2 | The angle KJL is congruent to the angle A | Copied using the procedure shown in Copying an angle. See that page for the proof. |

3 | The angle KLJ is congruent to the angle B | Copied using the procedure shown in Copying an angle. See that page for the proof. |

4 | Triangle JKL satisfies the side length and two angle measure given. |

- 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 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

(C) 2011 Copyright Math Open Reference.

All rights reserved

All rights reserved