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# 3. Angles – G3

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Lecture

In this mini-lecture, we cover Topic G3 on angles. In particular, we consider: (i) six types of angles at a point: acute angle, right angle, obtuse angle, straight angle, reflex angle, and complete angle; (ii) the properties of angles at a point on a straight line, where we define vertically opposite angles; (iii) corresponding and alternating angles on parallel lines; (iv) how we can use what we have learned to derive the sum of angles in a triangle, and (v) how to derive the angle sum in an n-sided polygon, including that of regular n-sided polygons.

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.

#### Cite this Lecture

APA style

Lotay, J. (2022, August 30). Properties and Constructions I – Edexcel GCSE (1MA1): Foundation Tier - Angles – G3 [Video]. MASSOLIT. https://massolit.io/courses/geometry-and-measures-properties-and-constructions-i-pearson-edexcel-gcse-mathematics-9-1-foundation-tier/angles-g3-6005392e-184b-41c4-9ce8-7536cc1ed05d

MLA style

Lotay, J. "Properties and Constructions I – Edexcel GCSE (1MA1): Foundation Tier – Angles – G3." 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/angles-g3-6005392e-184b-41c4-9ce8-7536cc1ed05d