TeXipedia

triangle

Represents an equilateral triangle shape, commonly used in geometric proofs and mathematical notation.

Overview

Essential in geometric expressions and mathematical demonstrations, particularly when discussing triangle-related theorems, properties, or relationships.

  • Frequently appears in elementary geometry and trigonometry.
  • Used to denote triangle operators or transformations in advanced mathematics.
  • Common in proofs involving similar or congruent triangles.
  • Appears in physics and engineering diagrams to represent change or difference (especially when discussing variations).
  • Often employed in set theory to denote symmetric difference between sets.

Examples

Defining the area of a triangle using its base and height.

A=12bhwhere △ABC has base b and height hA = \frac{1}{2}bh \quad \text{where } \triangle ABC \text{ has base } b \text{ and height } h 
A = \frac{1}{2}bh \quad \text{where } \triangle ABC \text{ has base } b \text{ and height } h

Stating the triangle inequality theorem for sides a, b, and c.

In △ABC:a+b>c,  b+c>a,  a+c>b\text{In } \triangle ABC: a + b > c, \; b + c > a, \; a + c > b 
\text{In } \triangle ABC: a + b > c, \; b + c > a, \; a + c > b

Expressing the angle sum property of a triangle.

For any △: α+β+γ=180∘\text{For any } \triangle \text{: } \alpha + \beta + \gamma = 180^\circ 
\text{For any } \triangle \text{: } \alpha + \beta + \gamma = 180^\circ