Sides
Name the figure
Equilateral, isosceles, or scalene. The side names come first.
Independent geometry notebook
Systems of triangles, drawn and named.
TrigoSystems is a structured set of notes for triangular geometry: classification, congruence, right-triangle ratios, and the two laws that govern any three-sided figure. Work the figures. Name what you see. The rest follows.
Angles
Read the corners
Acute, right, or obtuse. Interior angles always close at 180°.
Ratios
Compare the parts
Sine, cosine, and tangent turn an angle into a comparison of sides.
Curriculum
Six modules
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.