Students use geometric reasoning to establish relationships between angles in particular types of polygons.

This sequence is for students who:

- have a sound understanding of the types and measure of angles.
- have knowledge of the angle sum of a polygon. This can be developed as needed during the first lesson.

Elementary algebra is helpful to prove the results relating to 90°-270° polygons in the first lesson.

### Lesson 1: 90°-270° Polygons

Students draw polygons that contain only 90° and 270° angles. They establish a relationship between the number of 90° and 270° angles, and prove their result using the angle sum of a polygon. They generalise the result to any number of sides.

### Lesson 2: Arranging Angles

Students look at how many different ways they can arrange the angles in a 90°-270° decagon. They explain their reasoning using the number of different ways that they can partition numbers into two parts. The lesson offers opportunities for students to be creative in how they arrange the angles and has the potential for students to use coding to construct rectilinear polygons.

### Lesson 3: Maximum Number of 90°-270° Angles

Students construct polygons containing a large number of 90° angles or a large number of 270° angles. They make generalisations about the maximum number of 90° or 270° angles in any given polygon, and justify their generalisations using the angle sum of a polygon. There are opportunities to construct polygons using the coding program Scratch.

Last updated June 21 2020.