## Prologue

- Ontario Grade 8
- Curriculum and Connections: Patterning and Algebra
- "Sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation and using a variety of tools"

- Ontario Curriculum
- 8m40 (Overall Expectations) demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world
- 8m41 (Overall Expectations) develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles
- 8m43 (Geometric Properties) sort and classify quadrilaterals by geometric properties, including those based on diagonals
- 8m45 (Geometric Properties) investigate and describe applications of geometric properties in the real world

- Curriculum and Connections: Patterning and Algebra

## Act I

- Is there a way to fold a triangle so that it can be cut out by using only one cut?

## Act II

- Suggest attempting a simpler problem. Ironically, both of the following are easier.

- Or maybe watch one failed attempt at cutting a triangle out in one cut

## Act III

- One possible solution for cutting out the triangle in one cut (view as image)

## Sequel

- Try cutting out a parallelogram in one cut. Try other polygons.

- Can you cut out the letters of the alphabet using this theorem?
- Check out Erik Demaine's awesome site
- Numberphile explains the "Fold and Cut Theorem"

https://www.youtube.com/watch?v=ZREp1mAPKTM