Statically determinate truss?The 10-second check

Why does it work? (30 seconds)

• Every joint has 2 equations — ΣFx and ΣFy → 2j equations in total. (There is no moment equation: all the forces at a joint meet at one point.)
• The unknowns: the force in every member (m) and every reaction (r).
• Equations = unknowns → equilibrium alone solves everything.

2 trusses, 10 seconds each

• Truss 1
  9 members, 3 reactions, 6 joints → 9 + 3 = 12 = 2·6 determinate ✓
• Truss 2
  The zero-force-member truss: 15 + 3 = 18 = 2·9 determinate ✓

That's it. Both trusses are determinate — you can start solving.

3 counting traps

• A pinned support as one reaction. You get 9 + 2 = 11 < 12 → "mechanism" by mistake, and you stop a solvable exercise.
• Forgetting joints on the supports. They are joints too.
• Counting a roller support's reaction twice. Roller = one reaction, perpendicular to the surface.

For the advanced: The equality is necessary, but not always sufficient — if one part has a redundant member and another part lacks a diagonal, the structure will still fold.