# Polygons, Circles, Transformations & Data

- Created by: Kathryn
- Created on: 10-05-14 09:17

## Polygons

## Special Types of Triangles

*Equilateral* - All 3 sides equal and all 3 angles equal (to 60^{0}).

*Isosceles* - Two sides the same and the angles at the bottom of those sides are equal.

*Scalene* - No sides or angles equal.

**You can also classify triangles by their angles :**

*Acute-angled* - All angles are acute (less than 90^{0}).

*Right-angled* - One angle is 90^{0}.

*Obtuse-angled* - One angle is obtuse (greater than 90^{0}).

The area of a triangle is

## Quadrilateral

**Square** - All sides equal, all angles 90^{o}, 4 lines of symmetry, rotation symmetry of order 4.

**Rectangle** - Two pais of equal and parallel sides, all angles 90^{o}, two lines of symmetry, rotation symmetry of order 2.

**Rhombus** - All sides equal, opposite sides parallel, two lines of symmetry, rotation symmetry of order 2. (Basically a square leaning over. Sometimes referred to as a diamond!

**Parallelogram** - Two pairs of equal and parallel sides, opposite angles equal, no lines of symmetry, rotation symmetry of order 2. (Basically a rectangle leaning over.).

**Trapezium** - One pair of parallel sides, no symmetry.

**Kite** - Two pairs of equal sides next to each other, one line of symmetry, no rotation symmetry

## Gathering Data

There are two types of number data: **Discrete** and **Continuous**.

**Discrete** data can only take specific values and not the values in-between.

**Continuous** data can take any value within your range of accuracy.

*Questionnaires*

- Questions must be specific.
- Questions must not be leading.

## Analysing Data

**Mean** is the total of all the items divided by the number of items.

**Median** is the middle value.

**Mode** is the most common value.

**Range** is the difference between the smallest and the biggest value.

*Grouped data*

**Mean** - assume all the items in a group take the **mid-point** of the group so for each group you do **mid-point x frequency**. Add them all up and divide by the **Total Frequency**.

**Median** - you cannot find the median, only the group that it is in.

**Modal group** - the group with the highest frequency.

*Note:* if there are an even number of items then there will be two middle values so the median will be halfway between them.

## Pie Charts

**To work out the angle needed for each section:**

*Reading Pie Charts*

**To find out the frequency that each section represents, measure the angle for the section then:**

## Other Charts/Diagrams

*Frequency Diagrams*

These are sometimes called **bar charts**.

These are a good way of looking at the **spread** of data and are very easy to draw.

*Line Graphs*

Line Graphs are only used for discrete data and are simply a line (instead of a bar) for each data value showing total frequency.

## Scatter Diagrams

Simply plot crosses on a graph for the two things you are looking at.

If the data follows a 'trend' or '**correlation**' we can draw a **line of best fit** showing the general slope of the data.

You can then get further information from the graph by using your line of best fit.

## Cumulative Frequency

*Key Points*

- Cumulative frequency simply means adding the frequencies up as you go along.
- When plotting the graph, always plot points using the
**upper value**of each group. - Cumulative frequency is always plotted on the vertical axis (up the side) and the range of data goes across the bottom.
- The shape of a cumulative frequency curve looks like a 'stretched S' and is called an
**ogive**.

The more 'stretched-out' the 'S' is the more spread out the data is. An 'S' with a very steep middle section indicates the data being tightly grouped around the median.

**Median**- go halfway up the cumulative frequency axis, read across and down then read the median from the**bottom scale**.**Lower Quartile**- go a quarter of the way up the cumulative frequency axis, read across and down then read the Lower Quartile from the**bottom scale**.**Upper Quartile**- go three-quarters of the way up the cumulative frequency axis, read across and down then read the Upper Quartile from the**bottom scale**.**Inter-Quartile Range**- the difference between the Lower Quartile and the Upper Quartile.

## Transformations & Similar Shapes

**Reflection**- mirror line.**Rotation**- angle, direction, centre.**Enlargement**- scale factor, centre.**Translation**- vector.Similar shapes are enlargements of one another. Similar shapes have the same angles and sizes proportionate.

This is not the same as another tricky maths word -**congruent.**Two shapes are congruent if they are exactly the same! Same sides, same angles, same everything!**1.**Always use corresponding sides when you work out the scale factor.**2.**Don't forget that in enlargements**the angles don't change!**

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