Dr J Frost (jamie@drfrostmaths.com) @DrFrostMaths KS3/GCSE: 2D Shapes Dr J Frost (jamie@drfrostmaths.com) @DrFrostMaths Objectives: Be able to classify 2D shapes and reason about their properties. Last modified: 8th October 2019

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STARTER: Identifying 2D polygons ! A polygon is a 2D shape with straight sides. ? Sides: 3 Triangle Equilateral ? Isosceles ? Scalene ? 4 ? Square Rectangle ? Rhombus ? Quadrilateral ? Parallelogram ? Trapezium ? Kite ? Arrowhead ? 5 Pentagon ? 8 12 Octagon ? Dodecagon ? 6 Hexagon ? 9 20 Nonagon ? Icosagon ? 7 Heptagon ? 10 Decagon ?

Properties of quadrilaterals Diagonals always equal in length? Diagonals always perpen- dicular? Shape Name Minimum Lines of symmetry Minimum num pairs of parallel sides Square Rectangle Kite Rhombus Parallelogram Arrowhead ? 4 2 1 ? 2 Yes No ? Yes No ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Click to Start Bromanimation A big debate we had in the maths office… Is a square a trapezium? It depends on the definition: “A trapezium is a quadrilateral with exactly one pair of parallel sides.” or “A trapezium is a quadrilateral with at least one pair of parallel sides.” A square would be a trapezium under the second definition. It seems odd that we might consider shapes with two pairs of parallel as trapeziums (as we’d usually call them parallelograms), but otherwise we’d have the following situation… Click to Start Bromanimation Trapezium? NO YES This lack of continuity (i.e. not being a trapezium for one specific case) is considered a bad thing in maths, so the weight of evidence is that a square IS a trapezium, and thus the second definition is the correct one.

Categorising Activity Shape Description 2D Shape Polygon A 2D shape with straight edges. Ellipse (Also known as an oval) Circle Quadrilateral Polygon with four edges. Square Regular polygon with four edges. Rectangle Two pairs of parallel sides, all angles equal. Oblong All rectangles which are not squares. Trapezium Quadrilateral with at least one pair of parallel sides. Parallelogram Quadrilateral with two pairs of parallel sides. Rhombus Quadrilateral with all edges the same length. Kite Quadrilateral where sides in adjacent pairs are equal in length. Arrowhead Kite with a reflex angle. Trapezium Square We’ve seen that all squares are trapeziums. We might use the arrow to mean “is a type of”. Using a full page of your book, form a ‘tree’ of all the shape classifications on the right. You may work in pairs. ‘2D Shape’ should be at the top of your tree/page, i.e.: Fro Tip: To see if for example all squares are rectangles, see if a square satisfies the definition of a rectangle. 2D Shape Polygon

Solution 2D Shape Polygon Ellipse Quadrilateral Circle Trapezium Kite Parallelogram Arrowhead Rhombus Rectangle Square Oblong