Similarity and congruence
Congruent: same shape AND size. Similar: same shape, possibly different size. Scale factor links similar shapes.
Two triangles are congruent (RHS, SAS, SSS, ASA/AAS) when corresponding parts match. Similar triangles have the same angles and sides in proportion. Higher: area scales by k², volume by k³.
Worked examples
Triangle similar with scale factor 3: sides ×3, area ×9, volume ×27.
Two triangles are congruent if SSS, SAS, ASA/AAS or RHS match.
If A = 30°, B = 60° in triangles ABC and DEF, and a/d = b/e then triangles are similar (AA).
Frequently asked questions
Why area scales by k²?
Area is two-dimensional; doubling each side quadruples the area.
Why volume by k³?
Three dimensions; tripling each side gives 27× the volume.