(From Tiffin Year 7 scheme of work)
(a) Apply Pythagoras' Theorem to single right-angled triangles.
(b) Appreciate that an answer in surd form is exact.
(c) Know common Pythagorean triples: (3,4,5), (5,12,13) and multiples of these.
(d) Solve more advanced problems involving use of Pythagoras' Theorem:
* Finding the perpendicular height and area of an isosceles and equilateral triangle (and a mental method for the latter).
* Multiple right-angled triangles with shared sides.
* Appreciate that we sometimes need to add lines to yield right-angled triangles.
* Use of algebraic sides.
* Appreciate that a triangle with angles 30-60-90 is half an equilateral triangle, using this to reason about sides.
Recaps basic trigonometry for right-angled triangles, exact trigonometric values, more complicated problems (e.g. involving surds) and 3D Pythagoras/trigonometry.
Covers geometric problems (involving lengths, angles and area) found in Intermediate Maths Challenges and Olympiads.