Congruence

This course is a part of Mathematics I, a 16-course Topic series from Khan Academy.

Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms.

This course contains 7 segments:

Transformations & congruence

Two figures are congruent if you can go from one to another through some combination of translations, reflections and rotations. In this tutorial, we'll really internalize this by working through the actual transformations.

Triangle congruence

Learn how the definition of congruence using rigid transformations can be simplified to simple criteria when studying congruent triangles.

Theorems concerning triangle properties

Now that we know how to show that two triangles are congruent, let's put that to use by proving some theorems about triangles.

Working with triangles

Learn how to solve different geometric problems using triangle congruence.

Theorems concerning quadrilateral properties

Triangle congruence is not only useful when working with triangles, it's also useful with any other kind of polygon! Prove a few theorems about the properties of parallelograms using triangle congruence.

Proofs of general theorems that use triangle congruence

Gain even more experience with using triangle congruence in proofs.

Constructing bisectors of lines & 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).