# Kite Maths

## Introduction

### Explore Geometry With Kites!

Can you make a kite shape from a single A4 size sheet of paper using only three folds? Click Here to find out how.

Will your kite tessellate? Can you put a number of kites together to make a symmetric design? What about 4 lines of symmetry and rotational symmetry of order 8.... is it possible?

Can you write a procedure in Logo to draw a kite .... what designs can you make with your Logo kites?

### What is a kite?

In geometry a kite, sometimes known as a deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides. A kite can also be described as a quadrilateral with an axis of symmetry along one of its diagonals.

A kite, as defined above, may be either convex or concave, but the word "kite" is often restricted to the convex variety. A concave kite is sometimes called a "dart" or "arrowhead".

## Instructions

### Fold an A4 sheet of paper to make a kite!

 Step 1 Step 2 Step 3 Step 4

## Activities

### Challenges and investigations with Kites!

Activity 1
Fold a kite from an A4 sheet of paper by following the given instructions. What type of symmetry does your kite have?
Activity 2
Make seven more kites from sheets of A4 paper. Put your eight kites together to make different patterns. Can you work out the interior angles of the kite from the ways they fit together?
Activity 3
Make a kite from an A5 sheet of paper (half an A4 sheet). Will the smaller kite be half the width of the first kite you made? half the area? Will it's angles be the same?
Activity 4
Can you put a number of kites together to make a symmetric design with 4 lines of symmetry and rotational symmetry of order 8? Is it possible?
Activity 5
Use a computer such as Logo or Geogebra to create patterns with kites.
Activity 6
You can fold an A4 sheet of paper to make a pentagon too. Click here to find out how.

## Logo

### Use a computer to draw kites!

Here is a Year 8 student's design

to kite :size
lt 22.5
fd :size * 1.85
rt 67.50
fd :size
rt 90
fd :size
rt 67.5
fd :size * 1.85
rt 157.5
pu
fd 10
fill
bk 10
pd
end

to design
setfillcolor 7
kite 55 rt 45
setfillcolor 1
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 1
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 0
kite 55 rt 45
setfillcolor 7
kite 55 rt 45
setfillcolor 0
kite 55 rt 45
setfillcolor 10
repeat 8 [kite 35 rt 45]
end

Here are sole more designs made with Logo