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4. Triangles – G4, G5, G6
About this Lecture
In this mini-lecture, we cover the part of Topic G4 on triangles, Topic G5 on basic triangle congruence criteria, and the part of Topic G6 on triangle congruence and similarity. In particular, we focus on: (i) four types of triangles: equilateral triangle, isosceles triangle, right triangle (with hypotenuse), and scalene triangle; (ii) defining what it means for two triangles to be congruent; (iii) the four triangle congruence tests used to determine whether two triangles are congruent: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and right hypotenuse side (RHS); (iv) defining what it means for two triangles to be similar using side-length ratios and by comparing angles; (v) characterising triangles by angle (acute-angled versus obtuse-angled triangles); and (vi) properties of isosceles triangles, where we show that the base angles in an isosceles triangle are equal and that the bisector of the third angle is the perpendicular bisector of the line between the two base angles.
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 - Triangles – G4, G5, G6 [Video]. MASSOLIT. https://massolit.io/courses/geometry-and-measures-properties-and-constructions-i-pearson-edexcel-gcse-mathematics-9-1-foundation-tier/triangles-g4-g5-g6-a156fe83-d242-4595-9273-19869697ce44
Lotay, J. "Properties and Constructions I – Edexcel GCSE (1MA1): Foundation Tier – Triangles – G4, G5, 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/triangles-g4-g5-g6-a156fe83-d242-4595-9273-19869697ce44