triangle (idea)

An important definition in geometry about triangles is that the three vertices of any triangle are non-collinear. Which means the corners do not lie on the same line. This useful definition is often needed for many theorems about triangles to hold, including the uniqueness of barycentric coordinates in regard to a triangle.

Types of triangles:

• equilateral triangle - All sides are congruent.
• isosceles triangle - Two sides are congruent.
• scalene triangle (yet to be noded) - No two sides are congruent.
• right triangle - One angle is a right angle.

Some centers of triangles:

• incenter
• centroid
• orthocenter
• circumcenter
• nine point circle center - See: Nine Point Circle Theorem.

Theorems about triangles:

• Napoleon's Theorem
• Theorem of Snapper
• Pythagorean Theorem
• Nine Point Circle Theorem
• Hero's formula for the area of a triangle
• Theorem of Menelaus
• Theorem of Ceva

More triangle nodes!

• barycentric coordinates
• trilinear coordinates (yet to be noded)
• parallel postulate
• Euler line
• isogonal (YTBN)
• isotomic (YTBN)

/msg me for additions! Thanx.