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?

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".

Step 1 | Step 2 |

Step 3 | Step 4 |

- 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 program 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.

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 some more designs made with Logo

Click on an image below to see the full size animation. | |

It may take a while for Geogebra animations to load.

Lina Anagnos, Greece

Saturday, June 1, 2013

"I think that you could extend the activity by giving a kite constructed at a geogebra or Sketchpad file. It would be important for the students to connect the meanings of kite's area with the meaning of the diagonals. Another aim is the understanding of the shape reflections."

Transum,

Tuesday, October 25, 2016

"Thanks Lina for the suggestion. A Geogebra page has now been added so that you can interact with the kites and learn about their properties."