Shape and Space Problems Year 8
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Examples
Page Ref 
Problem
Title 
Objectives
Ref 
Description 
Key Words 
181, 185 
Inner
Rectangle 
2D
Shape, Angle Properties of Quadrilaterals 
A cute
result about angles around a quadrilateral  suitable for investigation
with Dynamic Geometry 
Congruent,
Corresponding, Complementary 
183 
Isosceles
Triangle 
Angle
properties in a Triangle 
A
first, though nontrivial, 'proof' involving angles 
Angle
sum, Base angles, Proof 
183,
221 
No
Rights 
Angle
properties in a Triangle 
A very
simple first proof 'by contradiction' involving angles in a triangle 
Angle
sum, Proof, Bisector, Dynamic Geometry 
184 
Two
Triangles 
Transformations,
Deductions 
An
example of very simple geometric reasoning 
Proof,
Rotate, Identical, Congruent 
184, 189, 213 
Rectangle
Cut 
2D Shape, Symmetry, 
A nice trick to
cut any rectangle in quarters 
Scale
factor, Stretch, Map 
184, 185 
Card
Folding 
2D Shape, Symmetry, 
Deduce
the original shape of paper from the twice folded final shape. 
Reflect,
Congruent, Symmetry 
184, 185 
When
The Boat Comes In 
Triangles,
Proof 
The
sum of any 2 sides of a triangle is greater than the third, so... 
Geometric
property, Proof 
184,235 
Ratio
Cut 
Area,
Transformation 
A
simple transformation makes easy work of a rectangle division. 
Area,
Ratio, Height

187 
Triangle
Sections 
Triangles,
Proof 
Prove
a simple relation within a triangle, using areas 
Geometric
property, Proof 
185, 187 
LShape 
Area, Proof 
How to divide any
2rectangle 'composite' in half? 
Symmetry,
Proof, Bisect 
186, 187 
Cut
A Rectangle 
Triangles,
Quadrilaterals 
Make
a triangle from a rectangle, using a single cut... 
Geometric
property, Symmetry 
186, 189 
How
Many Triangles 
Triangles 
How
many different triangles can you make with a choice of 6 rods ? 
Geometric
property, Proof, Sequence, General term 
191 
The
Radius 
Congruence,
Similarity 
A
simple application of Similar triangles 
Congruent,
Similar 
191, 193, 217 
Triangle
Dissections 
Congruence,
Similarity, Enlargement 
A
series of puzzles concerned with dissecting equilateral triangles into
smaller parts 
Congruent,
Similar 
61, 81, 193, 215 
Pendants 
Similarity,
Enlargement 
'Area Factors'
under enlargement give quick answers to this problem 
Similar,
Enlargement, Scale factor 
198, 199 
Pyramid
Scorpion 
3D Shape, Nets

The
shortest route across a Pyramid ? 
Nets,
Face, Vertex, Perpendicular 
198, 199 
Polyball 
3D
Shape, Symmetry 
How many balls
can you get to touch one in the middle? 
Plan
view, Plane, Symmetry 
200, 207 
TetraCubes 
3D Shape 
Identify shapes,
then use to build mini
Soma Cubes 
Plan,
View, Symmetry 
203 
Move
That Flag 
Transformations 
Use 2
reflections to effect a translation 
Image,
Translate, Reflect 
213 
Square
in a Triangle 
Transformations,
Symmetries 
How to
squeeze the largest possible square inside any triangle? 
Enlargement 
215, 221 
Forensic
Triangles 
Constructions, Dynamic Geometry 
Reconstruct the
original triangle from the sides' midpoints 
Medians,
Similar, Parallel 
221 
Eggs 
Constructions,
Compasses 
Take
an egg... 
Compasses, Perpendicular, Arc, Tangent 
221,
223 
Triangle
in a Square 
Constructions,
Dynamic Geometry 
How
to squeeze the largest possible equilateral triangle inside a square? 
Compasses, Rotation 
223, 245 
Height
of the Tower 
Similar Triangles,
Scale Drawing 
There's a tower,
see, across this river, and what you've got to do is... 
Similarity,
Elevation 
133, 227, 234 
Overlapping
Squares 1 
Loci,
Graphs, 2D shape 
This problem offers an
element of surprise in that the locus of possible solutions isn’t the
straight line that pupils may well expect 
Region,
Proof, Locus 
144,
229 
Britain
Rules The Weights? 
Binary, Imperial weights 
Metric weights aren't quite as
efficient as you would hope... 
Power,
Gram, Ounce 
233 
Anglesey 
Bearings 
Which is which
village?  using points of the compass. 
Points
of the compass 
235 
Trapezium
Cuts 
2D
Shape, Quadrilaterals, Area 
Dividing a
trapezium in several different ways  excellent for area calculations 
Area,
Base, Intersection 















