Constructing a 30° angle
Geometry construction using a compass and straightedge
This page shows how to construct (draw) a 30 degree angle with compass and straightedge or ruler. It works by first creating a
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.
Printable step-by-step instructions
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 a rhombus.
Its two diagonals form four 30-60-90 triangles.
The image below is the final drawing above with the red items added.
||Line segments PT, TR, RS, PS, TS are congruent (5 red lines)
||All created with the same compass width.
||PTRS is a rhombus.
||A rhombus is a quadrilateral with four congruent sides.
||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.
||Line segment AS is half the length of PS
||PS is congruent to TS. See (1), (3)
||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).
||Angle APS has a measure of 30°.
||In any triangle, smallest angle is opposite shortest side.
Try it yourself
Click here for a printable worksheet containing two 30° angle exercises.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Constructions pages on this site
Circles, Arcs and Ellipses
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