Geometric Addition of Vectors: Triangle Rule

This GeoGebra activity dynamically demonstrates the geometric addition of vectors using the head-to-tail triangle rule, showing how two vectors sum up to a resultant vector. The core mathematical concepts covered include geometric vector representation, translation of free vectors, and the commutative and associative properties of vector addition. In terms of construction, the tool uses the `Vector` command to define $u$ and $v$, and the `Line` and `Intersect` commands to translate vectors and find key points $A, B, C, D$, generating $u'$, $v'$, and the sum vector $w$. This is highly suitable for high school coordinate geometry, trigonometry, or introductory college linear algebra courses to visualize vector operations.