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.
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Other constructions pages on this site
Circles, Arcs and Ellipses
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