(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.
GCSE question compilation which aims to cover all types of questions that might be seen on the topic of Pythagoras' theorem. Students can complete this set of questions interactively on the DFM Homework Platform. Also contains answers.