Chapter 7: Triangles

Triangles is where congruence — only recognised informally back in Class 8 — gets proved rigorously for the first time, using the criteria SSS, SAS, ASA and RHS, alongside isosceles-triangle properties and triangle inequality rules (the sum of any two sides must exceed the third, so 3, 4 and 9 could never form a triangle).

Naming a congruence with vertices in the wrong correspondence (writing △ABC≅△DEF when the actual matching is different) silently invalidates an otherwise correct proof — a mistake worth double-checking every time. Assuming matching angles alone (AAA) proves congruence is another common trap; it only proves similarity, the idea Class 10's Similar Triangles chapter is built around instead.