likformiga

Likformiga is a geometric term used to describe figures that share the same shape but may differ in size. Two plane figures are likformige (similar) if there exists a correspondence between their vertices such that corresponding angles are equal and the lengths of corresponding sides are proportional by a constant factor. Equivalently, one figure can be obtained from the other by a similarity transformation, which combines translation, rotation, reflection and uniform scaling.

Key properties: the constant of proportionality is the similarity (scale) factor k. Each length in the first figure is multiplied by k to obtain the corresponding length in the second. For polygons, areas scale by k^2, while perimeters scale by k. If k>1 the second figure is larger; if 0<k<1 it is smaller. If the transformation preserves orientation, the similarity is direct; if it reverses orientation, it is indirect.

Examples: the triangles with sides 3,4,5 and 6,8,10 are likformige with k=2, as are any two similar polygons whose corresponding angles are equal and whose sides are in proportion.

In triangles, common criteria guarantee similarity: AA (two equal angles implies all angles are equal), SAS (two sides in proportion with the included angle equal), and SSS (all three sides in proportion).

Applications include geometry problem-solving, computer graphics, architectural design and map projections. The study of likeness in shape under scaling is foundational to understanding how objects can be compared and transformed without altering their form. See also similarity (geometry), dilation, congruence, transformation.