Geometric constructions

This course is a part of Geometry (all content), a 17-course Topic series from Khan Academy.

We now have fancy computers to help us perfectly draw things, but have you ever wondered how people drew perfect circles or angle bisectors or perpendicular bisectors back in the day. Well this tutorial will have you doing just as your grandparents did (actually, a little different since you'll still be using a computer to draw circles and lines with a virtual compass and straightedge).

This course contains 4 segments:

Constructing bisectors of lines and angles

With just a compass and a straightedge (or virtual versions of them), you'll be amazed by how many geometric shapes you can construct perfectly. This tutorial gets you started with the building block of how to bisect angle and lines (and how to construct perpendicular bisectors of lines).

Constructing regular polygons inscribed in circles

Have you ever wondered how people would draw a square, equilateral triangle or even hexagon before there were computers? Well, now you're going to do just that (ironically, with a computer). Using our virtual compass and straightedge, you'll construct several regular shapes (by inscribing them inside circles).

Constructing circumcircles and incircles

In our study of triangles, we spent a decent amount of time think about incenters (the intersections of the angle bisectors) and circumcenters (the intersections of the perpendicular bisectors). We'll now leverage this knowledge to actually construct circle inscribed and circumscribed about a triangle using only a compass and straightedge (actually virtual versions of them).

Constructing a line tangent to a circle

Learn how to construct tangents to circles with certain conditions using compass and straightedge. For example, draw the tangent to a given circle that passes through a given point.