Geometry is the study of shapes, sizes, positions, and properties of space. It develops logical reasoning through formal proofs.

Key Topics

• Euclidean Geometry — Points, lines, planes, angles, and the axioms that govern them.
• Triangles — Congruence, similarity, the Pythagorean theorem \(a^2 + b^2 = c^2\), and trigonometric ratios.
• Circles — Arcs, chords, tangents, secants, and the relationship \(C = 2\pi r\).
• Polygons and Area — Properties of quadrilaterals, regular polygons, and area formulas.
• Solids and Volume — Prisms, cylinders, pyramids, cones, and spheres.
• Transformations — Translations, rotations, reflections, and dilations.
• Coordinate Geometry — Using algebra to solve geometric problems on the coordinate plane.
• Proofs — Two-column, paragraph, and indirect proofs — the heart of mathematical reasoning.

Why It Matters

Geometry is everywhere: architecture, engineering, computer graphics, and art. The proof-based thinking it demands is the same kind of reasoning used in law, philosophy, and computer science.