Geometric Shapes#
Definition: Geometric Figure
A geometric figure in the Euclidean space \(\mathbb{R}^n\) is any subset \(G \subset \mathbb{R}^n\).
Similarity#
Definition: Similarity
Two Geometric Shapes \(G_1\) and \(G_2\) are similar iff there exists a transformation \(f\) which is a combination of a translation and a scaling such that
\[ f(G_1) = G_2 \qquad \text{ and } \qquad f^{-1}(G_2) = G_1 \]
Notation
\[ G_1 \sim G_2 \]
Congruence#
Definition: Congruence
Two Geometric Shapes \(G_1\) and \(G_2\) are congruent if there exists an [[Isometry]] which maps \(G_1\) onto \(G_2\).
Notation
\[ G_1 \cong G_2 \]
Intuition
The two geometric figures are congruent if there is a way to move and rotate one of them in such a way so as to make it coincide with the other figure.