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6. Basic Proofs and the Golden Ratio – G6
About this Lecture
In this 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, which strengthens our understanding of how to derive results and write down proofs (Topic G6). As we move through this mini-lecture we consider: (i) triangle facts and triangle congruence; (ii) parallel line and quadrilateral properties; and (iii) triangle similarity and side-length ratios. This allows us to find the diagonal length of a regular pentagon with side lengths of one unit. This value is known as the Golden Ratio and is found in other areas of mathematics as well as in nature.
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).
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.
Cite this Lecture
Lotay, J. (2022, August 30). Properties and Constructions I – Edexcel GCSE (1MA1): Foundation Tier - Basic Proofs and the Golden Ratio – G6 [Video]. MASSOLIT. https://massolit.io/courses/geometry-and-measures-properties-and-constructions-i-pearson-edexcel-gcse-mathematics-9-1-foundation-tier/basic-proofs-and-the-golden-ratio-g6-21b65e03-9a74-4df2-9f19-855969d6f4e1
Lotay, J. "Properties and Constructions I – Edexcel GCSE (1MA1): Foundation Tier – Basic Proofs and the Golden Ratio – G6." MASSOLIT, uploaded by MASSOLIT, 30 Aug 2022, https://massolit.io/courses/geometry-and-measures-properties-and-constructions-i-pearson-edexcel-gcse-mathematics-9-1-foundation-tier/basic-proofs-and-the-golden-ratio-g6-21b65e03-9a74-4df2-9f19-855969d6f4e1