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Need to Know
Need to Know

Geometry

The angle facts and theorems you must have ready.

How to use this: say each rule in your head, then tap Show me to check.

Angle facts

2 rules
Rule 01

On a line & crossing lines

Straight line: angles add to 180°. Vertically opposite angles are equal.

Rule 02

Parallel lines

Corresponding (F) equal · alternate (Z) equal · co-interior (C) add to 180°.

Triangles

2 rules
Rule 03

Angle rules

Angles add to 180°. Exterior angle = sum of the two interior opposite angles.

Rule 04

Special triangles

Isosceles: equal sides ⇒ equal base angles. Equilateral: all 60°.

Congruent triangles

1 rule
Rule 05

The four tests

  • SSS — three sides.
  • SAS — two sides + angle between.
  • ASA — two angles + side between.
  • RHS — right angle, hypotenuse, one side.

Parallelograms

1 rule
Rule 06

Properties

Opposite sides and angles equal; diagonals bisect each other; area = base × height.

Circle theorems

1 rule
Rule 07

The big ones

  • Centre angle = 2 × circumference angle (same arc).
  • Angle in a semicircle = 90°.
  • Cyclic quad: opposite angles add to 180°.
  • Tangent ⊥ radius.

Mathslive.ie · Geometry · Need to Know