## Prologue

• 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

## 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'sÂ awesome site
• Numberphile explains the "Fold and Cut Theorem"