Two subsets \(X\) and \(Y\) of Euclidean metric space \(\mathbb R^n\) are called congruent, if there exist an Euclidean movement (or a composition of such movements), that reversibly transforms every point of \(X\) into a point of \(Y\).
We call two segments on a straight line congruent, if they are identical in size and position, or if we can find one or more than one Euclidean movements (like translations and/or reflections) such that both segments become identical in size and position.
We call two plane figures (e.g. triangles, rectangles, trapezoids, circles) in a plane congruent, if they are identical in size and position, or if we can find one or more than one Euclidean movements (like translations, reflections and/or rotations) such that both figures become identical in size and position.
We call two solids (e.g. polyhedrons, spheres) congruent, if they are identical in size and position, or if we can find one or more than one Euclidean movements (like translations, reflections and/or rotations) such that both solids become identical in size and position.
Axioms: 1
Definitions: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Explanations: 18
Proofs: 19 20 21 22 23 24 25
Propositions: 26 27 28 29 30 31 32 33 34 35 36 37 38 39