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 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 2-D Shape, Quadrilaterals, Area Dividing a trapezium in several different ways - excellent for area calculations Area, Base, Intersection