3.1 Shapes and their properties
Shapes and their properties
Everything on shapes and their properties that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise shapes and their properties free
A worked example
Polygons · [1 mark]
What is the name of a polygon with 7 sides?
- B1Heptagon
The exam skills (5)
Polygons
- 3 triangle, 4 quadrilateral, 5 pentagon, 6 hexagon.
- 7 heptagon, 8 octagon, 9 nonagon, 10 decagon.
- Regular means all sides and all angles are equal.
Watch out: Mixing up hexagon (6) and heptagon (7).
Quadrilaterals
- Square and rectangle: four right angles.
- Parallelogram: two pairs of parallel sides. Rhombus: a parallelogram with all sides equal.
- Trapezium: one pair of parallel sides. Kite: two pairs of equal sides next to each other.
Watch out: Mixing up a rhombus and a kite.
Parts of a circle
- Radius: centre to edge. Diameter: edge to edge through the centre.
- Chord: edge to edge, not through the centre. Tangent: touches the outside once.
- Arc: part of the edge. Sector: a slice. Segment: cut off by a chord.
Watch out: Mixing up sector and segment.
3D shapes
- Faces are the flat surfaces, edges are where they meet, vertices are the corners.
- Imagine or sketch the shape and count each one.
- Check with Euler: faces + vertices − edges = 2.
Watch out: Counting the hidden faces at the back twice, or not at all.
Symmetry
- A line of symmetry is a fold line where both halves match.
- Rotational order: how many times it looks the same in one full turn.
- A regular polygon with n sides has n lines and order n.
Watch out: Saying order 0. Every shape has at least order 1.
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