Students learn how to construct a perpendicular bisector and equidistant path using a pair of compasses and ruler. As learning progress students are challenged to bisect a line at a given point and to find the shortest route between a point and a line.

The start of the lesson is used to recap constructing triangles involving side, side, side using a pair of compasses. The plenary challenges students to construct a scale drawing and use a perpendicular bisector to find the shortest route possible.

**Differentiated Learning Objectives**

- All students should be able to construct the perpendicular bisector of a line segment.
- Most students should be able to construct an equidistant path between two points.
- Some students should be able to recognise and use the perpendicular distance from a point to a line as the shortest distance to the line.