# Theory

The Triangle Inequality - Yr 7+. The inequality itself, the Reverse Triangle Inequality and a variety of applications. Easier questions More applications

Area of a quadrilateral - Yr 8+. Rectangle, square, trapezium, parallelogram, kite, rhombus. Includes proof that a kite's diagonals are perpendicular and one bisects the other.

Classifying Platonic solids - Yr 8+. Knowledge of angle sum at a point. VERY BRIEF NOTES.

Bonus - using geometry to estimate Earth's radius - Yr 9+ (not part of the curriculum). Knowledge of formula for circumference of circle required.

Heron's formula - Yr 10+. Proof and applications. Requires knowledge of Law of Cosines.

Pythagorean Inequality - Yr 10+. Requires knowledge of Law of Cosines.

# Questions

Lines of symmetry - Yr 4+.

Cuboid problem - Yr 5+. Knowledge of volume of a rectangular prism, factors and times tables, trial and error process.

Octagon problem - Yr 5+. Knowledge of congruence and familiarity with construction is a plus, but the problem diagram requires no special knowledge beyond the definition of an octagon.

Irregular shape - Yr 5+. Doable with good geometric/visual intuition but algebra is a plus.

Parts of a rectangle - Yr 6+. Knowledge of area of rectangle, triangle.

Trapezoid puzzle - Yr 7+. Knowledge of area of triangle, Pythagoras' theorem.

Triangle word problem - Yr 7+. Knowledge of area of a triangle, Pythagoras.

Counterintuitive areas problem - Yr 7+. Knowledge of Pythagoras' theorem, area of a triangle.

Irregular quadrilateral area - Yr 7+. Knowledge of Pythagoras, area of triangle. Familiarity with construction is a plus.

Touching circles puzzle - Yr 7+. Knowledge of Pythagoras.

Pentagon problem - Yr 7+. Angles, equilateral triangles.

Question in the style of Pythagoras Theorem proof - Yr 7+. Knowledge of algebra, area of a triangle. Would be nice to have familiarity with Pythagoras.

Triangles and ratios - Yr 7+. Knowledge of ratios, algebra.

Easy triangle problem - Yr 8+. Knowledge of angle sum of triangle, supplementary angles, isosceles triangles.

Quadrilateral with conditions on its angles - Yr 8+. Angle sum of quadrilateral.

Overlap puzzle - Yr 8+. Knowledge of percentages and equations.

Find the volume of a box from its net - Yr 8+. Algebra

Tricky trapezoid - Yr 8+. Knowledge of area of trapezoid, Pythagoras.

Angle between pencils - Yr 8+. Angle at a point, isosceles triangles.

Perimeter puzzle - Yr 8+. Corresponding angles.

Find the side length! - Yr 8+. Pythagoras application.

Annulus problem - Yr 9+. Knowledge of Pythagoras, triangle congruence, area of circle.

Composite shape - Yr 9+. Knowledge of area of circle, ratios.

Semicircles puzzle - Yr 9+. Knowledge of area of a circle, Pythagoras' theorem.

Area of sector - Yr 9+. Knowledge of area of circle.

Squaring the circle - Yr 9+. Knowledge of area of circle.

Star shape - Yr 9+. Knowledge of area of circle, area of rhombus nice but not necessary.

Circles inside circles - Yr 9+. Knowledge of Pythagoras, area of circle. Two puzzles.

Inscribed rectangle area puzzle - Yr 9+. Knowledge of area of circle, Pythagoras' theorem.

Perimeter word problem - Yr 9+. Ability to construct and solve equations, knowledge of percentages.

Stack of cubes - Yr 9+. Knowledge of surface area and volume of a cube. Visualisation skills/geometric thinking useful. Summation notation and knowledge of some basic summation results useful but not necessary.

Octahedron - Yr 10+. Knowledge of formula for volume of a pyramid, area of a rhombus.

Construction problem - Yr 10+. Angles, perimeter.

Equally spaced points around a circle - Yr 10+. Knowledge of congruence, angle sum of a quadrilateral.

Triangle vs hexagon - Yr 10+. Knowledge of Pythagoras, index laws, sine area formula would be nice.

Volume of water in a tank - Yr 10+. Pythagoras, trig, area of a circle.

Inscribed triangle problem - Yr 10+. Pythagoras, area of circle.

Hexagons and circles area problem - Yr 10+. Knowledge of sine area formula, area of a circle.

Triangle in a square problem - Yr 10+. Solving quadratics, area of a triangle.

Hexagon and triangle area puzzle - Yr 10+. Knowledge of cos rule, sine area rule, congruence. Alternatively - knowledge of area of hexagon.

Circle inscribed in rhombus - Yr 11+. Knowledge of Pythagoras, circle geometry (tangent meets radius at right angle), simultaneous equations.

Octagon problem - NEEEDS CLEANUP - Yr 11+. Trig.

Stack of cubes - Yr 11+. Knowledge of summation notation and some basic

Inscribed semicircle - Yr 11+. Knowledge of circle geometry (tangent meets radius at right angle), similarity, Pythagoras.

Tricky tangents - Yr 11+. Knowledge of circle geometry, Pythagoras, congruence.

Angle at centre of circle - Yr 11+. Circle geometry.

Cyclic quadrilateral problem - Yr 11+.