Congruence of Triangles

Every time two machine parts must fit, two roof beams must carry the same load, or a tiled floor must repeat a pattern without a single gap, someone has relied on congruence — figures that are exactly the same shape and size. In your O/L geometry, congruence is the tool that lets you prove two sides are equal or two angles are equal without ever measuring them. It is the backbone of geometric proofs, and once you trust it, riders that once looked impossible become a short, tidy argument.