This page shows how to construct (draw) a 30 degree angle with compass and straightedge or ruler. It works by first creating a rhombus and then a diagonal of that rhombus. Using the properties of a rhombus it can be shown that the angle created has a measure of 30 degrees. See the proof below for more on this.
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.
|1||Line segments PT, TR, RS, PS, TS are congruent (5 red lines)||All created with the same compass width.|
|2||PTRS is a rhombus.||A rhombus is a quadrilateral with four congruent sides.|
|3||Line segment AS is half the length of TS, and angle PAS is a right angle||Diagonals of a rhombus bisect each other at right angles. See Rhombus definition.|
|4||Line segment AS is half the length of PS||PS is congruent to TS. See (1), (3)|
|5||Triangle ∆PAS is a 30-60-90 triangle.||∆PAS is a right triangle with two sides in the ratio 1:2. (third side would be √3 by pythagoras).|
|6||Angle APS has a measure of 30°.||In any triangle, smallest angle is opposite shortest side.|