Part 2 of 5
Part 2 — Plane Geometry
Explore the geometry of flat surfaces — triangles, polygons, circles, transformations, and the elegant relationships between 2D shapes.
Plane geometry is the study of shapes, lines, and angles in two dimensions — the geometry of the flat page. It is both the most visually intuitive branch of geometry and the one with the deepest theoretical richness.
In this part you will work through triangles and their many special properties, regular polygons and their areas, the geometry of the circle, trigonometry, and the transformations that move and map shapes in the plane. Each chapter builds naturally on the last, developing a complete picture of two-dimensional space.
By the end of Part 2 you will have mastered the core toolkit of classical plane geometry and be ready to extend it into three dimensions.
Chapters in this Part
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3
Triangles→
A complete guide to triangles — congruence conditions, angle sum, Pythagoras' theorem, medians, altitudes, and angle bis…
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4
Quadrilaterals→
A complete guide to quadrilaterals — parallelograms, rectangles, rhombuses, squares, trapezoids, kites, and general poly…
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5
Regular Polygons and Areas→
Regular polygons, classic Euclidean constructions of inscribed polygons, and area formulas for all polygon types in Eucl…
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6
The Circle→
A complete guide to the circle in Euclidean geometry — arc and chord theorems, tangents, secants, and the Apollonius cir…
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7
Similarity and Proportion→
Similarity, ratio, and proportion — similar polygons, harmonic division, the Golden Ratio, the Silver Ratio, and constru…
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8
Trigonometry→
Master the geometry of triangles through trigonometric ratios — sine, cosine, and tangent — the sine and cosine rules, e…
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9
Euclidean Constructions→
Euclidean constructions with compass and straightedge — bisecting angles, drawing perpendiculars, constructing polygons,…
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10
Tessellations and Tilings→
Which shapes tile the plane and why — from the three regular tessellations through semi-regular tilings to aperiodic Pen…
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11
Loci→
Loci in Euclidean geometry — the set of all points satisfying a given condition. Standard loci, compound loci, and pract…