## Area Relationship Projects

Project 1:

Write a GSP sequence (similar to the one in triangle-animation) that will transform the given triangle ABC into a right angled triangle DEF. Click here for triangle ABC.

Project 2:

Given any irregular figure. Describe a procedure that can be used to reduce the figure to a triangle of equal area (NOTE: an explanation of how/why the procedure works is expected)

For a GSP script that performs the procedure for a pentagon or a hexagon click on the appropriate word.

Project 3:

Given a triangle ABC, with a point P on one of the sides, show how you can divide triangle ABC into any number of equal parts (begin with 4) using lines drawn through P. (NOTE: an explanation of how/why the procedure works is expected) You will notice that there are limits on the position of point P if you wish to ensure an interior division of triangle ABC.

For a GSP script that performs the procedure for four equal parts click here.

Project 4
:

Given a square ABCD, show how you can divide the square into any number of equal parts (begin with 5) using lines drawn through one of its corners. (NOTE: an explanation of how/why the procedure works is expected)

For a GSP script that performs the procedure for five equal parts click here.

Project 5:

Given a rectangle, show how you can divide it into any number of equal parts (begin with 3) using lines drawn through a point on one of its sides. (NOTE: an explanation of how/why the procedure works is expected)

For a GSP script that performs the procedure for three equal parts click here. You will notice that there are limits on the position of point P if you wish to ensure an interior division of rectangle ABCD.

For projects 6 and 7 you will need to understand how to construct a mean proportional. Click here for a discussion of the mean proportional and it construction.
Project 6:

Given a triangle ABC, show how you can divide triangle ABC into any number of equal parts (begin with 4) using lines drawn parallel to one of its sides. (NOTE: an explanation of how/why the procedure works is expected)

For a GSP script that performs the procedure for five equal parts click here.

Project 7:

Given a square ABCD, show how you can divide the square into any number of equal parts (begin with 5) using lines drawn parallel to one of the diagonals (HINT this project follows very closely from the previous project and project 4). (NOTE: an explanation of how/why the procedure works is expected)

For a GSP script that performs the procedure for five equal parts click here

### Some further project ideas:

1. You will find some further topics on related projects by clicking here.

2. The following reference has a number of further examples of similar constructions:

Angel, H., (1873) Practical Plane and Solid Geometry. G.P. Putnam's Sons: New York.

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