2. Ruler and Compass Construction – G2

About this Lecture

Lecture

In this mini-lecture, we discuss Topic G2 on ruler and compass construction, focusing in particular on: (i) what a ruler and compass allow us to do; (ii) how to construct the perpendicular bisector of a line segment; (iii) understanding that the perpendicular distance from a point to a line is the shortest distance to the line; (iv) how to construct a perpendicular to a given line at a given point; (v) how to construct an equilateral triangle; (vi) how to bisect a given angle; and (vii) what we cannot do with a ruler and compass, e.g. trisect an angle.

Course

In this course, Professor Jason Lotay (University of Oxford) discusses topics G1-G6 in the Pearson Edexcel GCSE (9-1) Mathematics (1MA1) Specification for Foundation Tier. In the first mini-lecture, we cover the conventional terms and notations used in geometry (Topic G1). In the second mini-lecture, we use ruler and compass construction to create perpendicular bisectors and bisect angles (Topic G2). In the third mini-lecture, we explore types of angles and how we can use the properties of angles at a point on straight lines and on parallel lines to prove useful identities (Topic G3). In the fourth mini-lecture, we look at triangles and show how to use triangle congruence tests (Topics G4, G5, G6). In the fifth mini-lecture, we introduce six important quadrilaterals and use our understanding of angles, bisectors, and triangles to prove properties of quadrilaterals (Topics G4, G6). In the sixth mini-lecture, we tie together all the concepts we have learned in this course to find the length of the diagonal in a regular pentagon with side lengths of one unit (Topic G6).

Lecturer

Jason Lotay is a Professor of Pure Mathematics at the University of Oxford. He has previously held academic positions at UCL, Imperial College London, and Berkeley. His research interests are in differential geometry, particularly related to special holonomy, minimal submanifolds, gauge theory and geometric flows, and instantons.