Activity Overview
This is the second activity in a series where students take a deeper dive into parabolas, beyond the shallow depths of factorise, expand and graph.
In this activity students use triangle congruence to prove the paper folding envelope is a parabolic curve and use algebra to determine the corresponding equation.
Watch the Activity Tutorial
Objectives
Students see the difference between a function (parabola) that is provided as a model compared with a theoretical result. They use triangle congruence, Pythagoras (distance between two points) and algebra to prove the theoretical result.
Vocabulary
- Perpendicular
- Bisector
- Envelope
- Parabola
- Model
- Triangle Congruence
- Focus
- Directrix
About the Lesson
Students use triangle congruence to prove the theoretical application of a parabola (and quadratic equation) to model the locus of a set of points. Students use language such as ‘focus’ and ‘directrix’ and the corresponding definition of a parabola. The activity video explains the importance of these properties through the context of a ‘fry-scraper’.