Below in italics are the outcomes for this unit. Please do not edit them. Use them as the headings for lessons. You can then add a couple of sentences to explain how to do the maths, you may add a picture or a link to a relevant site.

Introduction

Here's a short cartoon to help you understand some of the basic tools and uses of geometry.

Lesson 1

labelling and naming triangles (eg ABC) and quadrilaterals (eg ABCD) in text and on diagrams
using the common conventions to mark equal intervals on diagrams


Imagine trying to live in a country where you don’t know the language. It would be difficult to communicate even the most basic of things. That is why we need to use a universal language for mathematics, for example labelling and naming shapes are important so we all understand exactly what is being communicated.
For example, this is the interval AB:
AB.jpg





If I place another interval in, we have:
AB&AC.jpg
Now we have two intervals, which we can identify as AB and AC. So now if I mention AC, you know exactly which interval I am talking about.

Joining B and C, we get a triangle, which we will call ABC.
ABC.jpg
Again, it is vital to label points and use proper names to identify intervals, angles and shapes so that you can communicate effectively.

There are many other labels that we use in diagrams. One of the more common ones is the symbol for equal lengths. Put simply, a small line is places across all intervals that have equal length.

This diagram shows the quadrilateral ABCD and indicates that the interval AB is equal to the interval DC. This can be written as AB = DC.
ABCD3.png
The diagram below shows that AB = DC and that BC = AD. Note that two lines are used on BC and AD to indicate that they are equal to each other, but not equal to the other intervals marked; so as the diagrams get more complex, you can use three lines or more to indicate equal lengths.
ABCD4.png
Take this quiz to see how much you remember.

Lesson 2

recognising and classifying types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, scalene triangles, isosceles triangles and equilateral triangles)

Human blood is classified using two different methods:
• The ABO system uses the presence of antibodies and has the classifications A, B, AB and O
• The Rh system classifies a blood type as either positive or negative.
Using both, we get the blood types (like O+, AB-, etc).

Triangles can also be classified in two different ways – one based on the lengths (equilateral, isosceles and scalene) and the other based on angles (acute, obtuse and right-angled). Hence any triangle can be classified using both classification systems.

This is an activity classifying triangles based on side lengths. This one is based on angles.

Lesson 3

constructing various types of triangles using geometrical instruments, given different information
eg the lengths of all sides, two sides and the included angle, and two angles and one side


Below are some short videos on how to do particular constructions. Doing these correctly and remembering what to do in an exam WILL TAKE PRACTICE! Do more than one.
Constructing a triangle given three sides.
Constructing a triangle given two lengths and one angle.
Constructing a triangle given one length and two angles.

Lesson 4

distinguishing between convex and non-convex quadrilaterals (the diagonals of a convex quadrilateral lie inside the figure)

A polygon is any two–dimensional shape that is made up solely of straight lines (so a semi-circle is NOT a polygon). Convex polygons have vertices that point outwards while non-convex (or concave) polygons have vertices that point (or cave) inwards.
ABCDE.jpg
Convex Polygon

ABCDE2.jpg
Non-Convex Polygon

Another method to determine if a polygon is convex or non-convex is the diagonal test. If you draw lines between every vertice, all these lines will be inside the shape for a convex polygon; if any lie outside the shape, it is a non-convex polygon.
ABCDE3.jpg
All diagonals are inside

ABCDE4.jpg
Diagonal CE is outside

Lesson 5

investigating the properties of special quadrilaterals (trapeziums, kites, parallelograms, rectangles, squares and rhombuses) by using symmetry, paper folding, measurement and/or applying geometrical reasoning
classifying special quadrilaterals on the basis of their properties
investigating the line symmetries and the order of rotational symmetry of the special quadrilaterals

Here's a video on point or rotational symmetry.
Here's one about line symmetry in the world.

Lesson 6

constructing various types of quadrilaterals