Curriculum
Modules
Work in order if this is new material. Skip to the law you need if you already have classification and right triangles.
Module 01
Classification of triangles
Every triangular system is named twice: once by its sides, once by its angles. Those two names determine which tools you are allowed to use.
Module 02
Congruence and correspondence
Two triangles are congruent when one can be placed on the other by rigid motion. Correspondence of vertices is the whole game.
Module 03
Right triangles
A right angle splits the system into two legs and a hypotenuse. That split is the source of both Pythagoras and the three primary ratios.
Module 04
Trigonometric ratios
In a right triangle, each acute angle has three primary ratios. They convert an angle into a comparison of sides, and a comparison of sides into an angle.
Module 05
Laws of sines and cosines
Once a triangle is no longer right, the primary ratios are not enough. The two laws extend the same ideas to any triangular system.
Module 06
Area of a triangular system
Area is half the product of two sides and the sine of the included angle. Several equivalent formulas exist so you can start from whatever is given.