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

2. www.drfrostmaths.com Everything is completely free. Why not register?
Register now to interactively practise questions on this topic, including past paper questions and extension questions (including UKMT).
Teachers: you can create student accounts (or students can register themselves), to set work, monitor progress and even create worksheets.
With questions by:
Dashboard with points, trophies, notifications and student progress.
Questions organised by topic, difficulty and past paper.
Teaching videos with topic tests to check understanding.

3. 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 ?

4. 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 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

5. 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.

6. 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

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