How is geometric thinking useful?

Key questions

  1. 1

    What do we mean by geometry?

  2. 2

    How can Pythagoras’ Theorem be used?

  3. 3

    How are similar triangles useful?

  4. 4

    What can be deduced using our knowledge of simple shapes and angles?

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Resource type Title
Rich example Distance between points
Many ways problem In-betweens
Food for thought All about ratios


Resource type Title
Fluency exercise What type of triangle?
Package of problems Finding triangles
Package of problems The quintessential proof
Many ways problem Look before you leap
Many ways problem Proving Pythagoras
Scaffolded task A perfect fit
Food for thought A limiting circle theorem
Food for thought Quadrature of the lunes
Food for thought The spider and the fly (Part 1)
Food for thought The spider and the fly (Part 2)
Investigation Napkin
Bigger picture Fermat's last theorem
Bigger picture Pinning down $\pi$
Bigger picture Symmetry
Bigger picture Triangles are the strongest shape
Bigger picture What geometry means to me

Review questions

Title Ref
Can we find $\alpha$ if one length is twice another? R5365
Can we find a formula for an island's territorial waters? R5534
Can we find the areas within the semicircles? R6699
Can we find the point that divides a line in a given ratio? R9585
Can we show this triangle is right-angled and find its area? R5442
Can we show we have three corners of a rectangle? R5386
Can we use similar triangles to find this side? R5081
Given two tangents to a circle, can we find these lengths? R9792
How can we arrange regular polygons around a point? R6908
How far does this pool ball travel to reach the pocket? R8022
If a cone sits on this sphere, what 's the cone's volume? R9694
If a sphere contains this cuboid, what's the largest cube it can contain? R9973
If these centres lie on a line, why is the triangle isosceles? R8917
What are the sides of this square and this triangle? R8567
What area needs to be searched to find the ship? R7368
What fraction of the square is the pentagon? R5492
What is the area of a square containing a regular hexagon? R6408
What is the length of one of the sides of this hexagon? R6223
What is the surface area of this cuboid? R7565
What links this incircle and circumcircle? R9259
What's the ratio of the circle's area to the square's area? R8179
Why is this quadrilateral a rhombus but not a square? R6641