Mathslive.ie

GEOMETRY

Exam Cog
①ANGLE FACTS

Straight line → 180°   Vert. opposite → equal

Full turn → 360°

★ Label every angle you can before solving
②PARALLEL LINES

F corresponding = equal

Z alternate = equal

C co-interior = add to 180°

③TRIANGLES

3 angles → 180°

Exterior = sum of 2 interior opposite

Isosceles → equal base angles   Equilateral → 60°

⚠ Longest side is opposite the largest angle.
④CONGRUENT TRIANGLES

Equal in every way. Tests:

SSS · SAS · ASA · RHS

★ Prove congruent → then matching sides/angles are equal
⑤PARALLELOGRAMS

Opposite sides & angles equal

Diagonals bisect each other

Area = base × height

⑥CIRCLE — PARTS

Centre, radius, diameter (=2r), chord, arc, sector, tangent

⑦CIRCLE THEOREMS

Centre angle = 2 × circumference angle (same arc)

Angle in semicircle = 90°

Cyclic quad: opposite angles → 180°

Tangent ⟂ radius

⑧METHOD
  1. Mark all equal/known angles
  2. Name the fact you are using
  3. Solve step by step
⑨KEY WORDS

Axiom (no proof) · Theorem (proved) · Converse (swap if/then)

⑩WATCH-OUTS
⚠ State the reason for each step in a proof — reasons earn marks.