Shape and Space Problems Year 8            

To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problem-and-solution Word document.

Examples Page  Ref  Problem Title Objectives Ref Description Key Words
181, 185 Inner Rectangle 2-D 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 non-trivial,  '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 2-D Shape, Symmetry,  A nice trick to cut any rectangle in quarters Scale factor, Stretch, Map
184, 185 Card Folding 2-D 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 L-Shape Area, Proof How to divide any 2-rectangle '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' mid-points  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, 2-D shape This problem offers an element of surprise in that the locus of possible solutions isnít 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 2-D Shape, Quadrilaterals, Area Dividing a trapezium in several different ways - excellent for area calculations  Area, Base, Intersection


Send site mail to  or personal comments direct to with questions or comments about this web site.
Last modified: June 18, 2007