# Geometry — Concepts, Formulas, Shapes & Topics Guide

## TL;DR
Geometry is the branch of mathematics that studies points, lines, angles, shapes, and space — how figures are built, measured, and related. This hub maps every geometry topic into ten clusters: foundations (points, lines, planes), angles, parallel lines and transversals, triangles, quadrilaterals and polygons, circles, 3D solids, coordinate geometry, conic sections, and transformations — each linking to a full guide with formulas and worked examples.

## One Subject Behind Every Map, Building, and Screen
Every bridge that holds, every route a GPS draws, and every pixel placed on a screen rests on the same subject: geometry. It is the mathematics of where things are, how big they are, and how they fit together — and almost everything built or navigated depends on it.

This page is the starting point. Below, **geometry** is broken into ten topic clusters, each linking to a detailed guide. Use it as a map: start with the foundations, then branch into whichever area you need.

## What Is Geometry?
**Geometry** is the branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. The word comes from the Greek _geo_ ("earth") and _metron_ ("measure") — literally "earth-measurement," reflecting its origins in surveying land and tracking the stars.

At its core, geometry is built from three undefined foundations — the **point** (a position), the **line** (a straight, endless path of points), and the **plane** (a flat, endless surface). Everything else — angles, triangles, circles, solids — is defined from these three.

## The Branches of Geometry
Geometry splits into a few major branches, and the clusters further down map onto them:

- **Plane (Euclidean) geometry** — flat, two-dimensional figures: lines, angles, triangles, quadrilaterals, polygons, and circles.
- **Solid geometry** — three-dimensional figures: prisms, pyramids, cylinders, and their volume and surface area.
- **Coordinate (analytic) geometry** — shapes placed on the x–y plane, described by equations: slope, intercepts, lines, and conic sections.
- **Transformational geometry** — how figures move and resize: translations, reflections, rotations, dilations, and symmetry.

A reader new to the subject usually moves left to right across that list — foundations and plane figures first, then solids, then the coordinate plane.

## Foundations: Points, Lines & Planes
The vocabulary the rest of geometry is written in — the building blocks before any shape appears.

- [Lines in Geometry: Types & Examples](/content/math/geometry/lines/index.html)
- [Line Segment: Definition, Properties & Examples](/content/math/geometry/line-segment/index.html)
- [Plane Definition in Math: Meaning & Examples](/content/math/geometry/plane-definition/index.html)
- [Perpendicular Lines - Definition, Slope, Examples](/content/math/geometry/perpendicular/index.html)
- [Parallel Lines — Definition, Properties, Examples](/content/math/geometry/parallel-lines/index.html)
- [Perpendicular Bisector: Definition & Construction](/content/math/geometry/perpendicular-bisectors/index.html)
- [Segment Bisector: Definition, Types & Examples](/content/math/geometry/segment-bisector/index.html)
- [Congruent Lines: Definition, Properties & Examples](/content/math/geometry/congruent-lines/index.html)
- [Skew Lines: Definition, Distance & Examples](/content/math/geometry/skew-lines/index.html)
- [Coplanar: Definition, Points, Lines & Examples](/content/math/geometry/coplanar/index.html)
- [Collinear Points: Definition, How to Prove & Examples](/content/math/geometry/collinear-points/index.html)

## Angles
Where two rays meet. Angles are the hinge of plane geometry — naming them, measuring them, and pairing them up.

- [Types of Angles: Acute, Right, Obtuse, Reflex](/content/math/geometry/types-of-angles/index.html)
- [Types of Angles — Acute, Right, Obtuse, Reflex](/content/math/geometry/acute-angle/index.html)
- [45 Degree Angle: Definition & Construction](/content/math/geometry/45-degree-angle/index.html)
- [90 Degree Angle: Definition & Construction](/content/math/geometry/90-degree-angle/index.html)
- [What is Adjacent? Meaning, Adjacent Angles, Examples](/content/math/geometry/adjacent/index.html)
- [Adjacent Angles — Definition, Properties, Examples](/content/math/geometry/adjacent-angles/index.html)
- [Vertical Angles — Definition, Theorem, Proof, Examples](/content/math/geometry/vertical-angles/index.html)
- [Complementary Angles — Definition, Properties, Examples](/content/math/geometry/complementary-angles/index.html)
- [Supplementary Angles — Definition, Properties, Examples](/content/math/geometry/supplementary-angles/index.html)
- [Supplementary vs Complementary Angles — Side by Side](/content/math/geometry/supplementary-vs-complementary-angles/index.html)
- [Linear Pair of Angles: Definition & Axiom](/content/math/geometry/linear-pair-of-angles/index.html)
- [Congruent Angles: Definition, Theorems, Examples](/content/math/geometry/congruent-angles/index.html)
- [Vertex Angle: Definition, Formula, Examples](/content/math/geometry/vertex-definition/index.html)
- [Central Angle in Geometry: Definition, Formula, Examples](/content/math/geometry/central-angle/index.html)
- [Angle Addition Postulate: Formula & Examples](/content/math/geometry/angle-addition-postulate/index.html)
- [Angle Bisector: Properties & Construction](/content/math/geometry/angle-bisector/index.html)
- [Angle Bisector Theorem: Statement, Proof, Examples](/content/math/geometry/angle-bisector-theorem/index.html)

## Parallel Lines & Transversals
When a line crosses a pair of parallels, eight angles appear in fixed relationships — the engine behind most "find the missing angle" proofs.

- [Transversal — All 8 Angles and Pair Relationships](/content/math/geometry/transversal/index.html)
- [Corresponding Angles — Postulate, Pair Table, Examples](/content/math/geometry/corresponding-angles/index.html)
- [Alternate Interior Angles: Theorem & Examples](/content/math/geometry/alternate-interior-angles/index.html)
- [Alternate Exterior Angles: Theorem & Examples](/content/math/geometry/alternate-exterior-angles/index.html)
- [Same Side Interior Angles: Theorem & Examples](/content/math/geometry/same-side-interior-angles/index.html)
- [Consecutive Interior Angles: Theorem & Examples](/content/math/geometry/consecutive-interior-angles/index.html)

## Triangles & Congruence
The three-sided figure that every higher result is built on — its types, its theorems, and the rules that prove two triangles identical.

- [Types of Triangles — Classification Matrix](/content/math/geometry/types-of-triangle/index.html)
- [Isosceles Triangle - Definition, Types, Formulas](/content/math/geometry/isosceles-triangles/index.html)
- [Isosceles Right Triangle: Formulas & Examples](/content/math/geometry/isosceles-right-triangle/index.html)
- [Isosceles Acute Triangle: Properties & Examples](/content/math/geometry/isosceles-acute-triangle/index.html)
- [Isosceles Obtuse Triangle: Properties & Examples](/content/math/geometry/isosceles-obtuse-triangle/index.html)
- [Right Angled Triangle: Properties & Formulas](/content/math/geometry/right-angled-triangle/index.html)
- [Right Scalene Triangle: Properties & Examples](/content/math/geometry/right-scalene-triangle/index.html)
- [Pythagoras Theorem - Formula, Proof, Examples](/content/math/geometry/pythagoras-theorem/index.html)
- [Triangle Sum Theorem: Proof, Formula, Examples](/content/math/geometry/triangle-sum-theorem/index.html)
- [Exterior Angle Theorem: Statement, Proof, Examples](/content/math/geometry/exterior-angle-theorem/index.html)
- [Altitude of a Triangle: Formulas & Properties](/content/math/geometry/altitude-of-a-triangle/index.html)
- [Median of a Triangle: Properties & Formula](/content/math/geometry/median-of-a-triangle/index.html)
- [Similar Triangles: Theorems & Properties](/content/math/geometry/similar-triangles/index.html)
- [Congruent (Congruence) - Meaning, Definition, Examples](/content/math/geometry/congruent/index.html)
- [CPCTC: Meaning, Proof & Examples](/content/math/geometry/cpctc/index.html)
- [Angle Angle Side (AAS) Congruence: Proof, Examples](/content/math/geometry/angle-angle-side/index.html)

## Quadrilaterals & Polygons
Four-sided figures and beyond — their properties, areas, and how the shape family tree fits together.

- [Geometric Shapes: Types, Properties & Examples](/content/math/geometry/geometric-shapes/index.html)
- [Shapes in Geometry — Complete 2D and 3D Taxonomy](/content/math/geometry/shapes/index.html)
- [Parallelogram - Properties, Area, and Formulas](/content/math/geometry/parallelograms/index.html)
- [Rhombus: Properties, Area, and Perimeter](/content/math/geometry/rhombus/index.html)
- [Trapezoid: Properties, Area, and Formula Guide](/content/math/geometry/trapezoid/index.html)
- [Trapezium - Definition, Properties, Area and Examples](/content/math/geometry/trapezium/index.html)
- [Isosceles Trapezoid: Properties, Area & Examples](/content/math/geometry/isosceles-trapezoid/index.html)
- [Properties of a Rectangle: Sides, Angles & Diagonals](/content/math/geometry/properties-of-rectangle/index.html)
- [Properties of a Kite: Sides, Angles & Diagonals](/content/math/geometry/properties-of-kite/index.html)
- [Is a Square a Rectangle? Yes — Here's Why](/content/math/geometry/is-a-square-a-rectangle/index.html)
- [Difference Between Square and Rhombus Explained](/content/math/geometry/difference-between-square-and-rhombus/index.html)
- [Pentagon Shape - Properties, Area, and Perimeter](/content/math/geometry/pentagon-shape/index.html)
- [Hexagon Shape — Definition, Types, Properties, Area](/content/math/geometry/hexagon/index.html)
- [Interior Angles: Sum Formula & Examples](/content/math/geometry/interior-angles/index.html)

## Circles
The set of points an equal distance from a centre — its parts, its measurements, and its equation.

- [Parts of a Circle: Names, Definitions & Diagram](/content/math/geometry/parts-of-circle/index.html)
- [Radius of a Circle: Definition, Formula, Examples](/content/math/geometry/radius/index.html)
- [Diameter of a Circle — Formula, Examples, Properties](/content/math/geometry/diameter-of-a-circle/index.html)
- [Chord of a Circle: Formula, Theorems, Examples](/content/math/geometry/chords-of-a-circle/index.html)
- [Circumference of a Circle - Formula, Examples](/content/math/geometry/circumference-of-a-circle/index.html)
- [Area of a Circle: Formula, Derivation & Examples](/content/math/geometry/area-of-a-circle/index.html)
- [Sector of a Circle: Area, Arc Length, Perimeter](/content/math/geometry/sector-of-a-circle/index.html)
- [Arc Length: Formula, How to Find It, Examples](/content/math/geometry/arc-length/index.html)
- [Equation of a Circle: Standard & General Form](/content/math/geometry/equation-of-circle/index.html)
- [Tangent in Geometry — Definition, Formula, Examples](/content/math/geometry/tangent/index.html)

## 3D Solids & Mensuration
The jump from flat figures to objects with volume — prisms, pyramids, and cylinders, plus how to measure them.

- [Cylinder — Shape, Formula, Examples](/content/math/geometry/cylinder/index.html)
- [Rectangular Prism - Volume, Surface Area, Formulas](/content/math/geometry/rectangular-prism/index.html)
- [Triangular Prism - Volume, Surface Area, Formulas](/content/math/geometry/triangular-prism/index.html)
- [Triangular Pyramid: Volume, Surface Area & Faces](/content/math/geometry/triangular-pyramid/index.html)

## Coordinate Geometry
Geometry on the x–y plane — where shapes become equations and lines have slopes and intercepts.

- [X and Y Axis in a Graph: Origin & Quadrants](/content/math/geometry/x-and-y-axis/index.html)
- [Quadrants of Coordinate Plane - I, II, III, IV](/content/math/geometry/quadrant/index.html)
- [Slope of a Line - Formula, Calculation, Examples](/content/math/geometry/slope/index.html)
- [Slope Intercept Form: y = mx + b & Examples](/content/math/geometry/slope-intercept-form-of-a-line/index.html)
- [y = mx + b: Read Slope & Y-Intercept, Plot a Line](/content/math/geometry/y-mx-b/index.html)
- [Y Intercept: Definition, Formula & Examples](/content/math/geometry/y-intercept/index.html)
- [Intercept Form of a Line: Formula & Examples](/content/math/geometry/intercept-form/index.html)
- [Horizontal Line - Definition, Equation, and Slope](/content/math/geometry/horizontal-line/index.html)
- [Undefined Slope: Definition, Equation & Examples](/content/math/geometry/undefined-slope/index.html)
- [Slope of Perpendicular Lines: The −1 Rule](/content/math/geometry/slope-of-perpendicular-lines/index.html)
- [Parallel & Perpendicular Lines: Slope Rules](/content/math/geometry/parallel-and-perpendicular-lines/index.html)

## Conic Sections
The curves you get by slicing a cone — parabolas and ellipses, with their defining points.

- [Conic Sections: Types, Formulas & Equations](/content/math/geometry/conic-sections/index.html)
- [Parabola - Definition, Formula, Graph, Examples](/content/math/geometry/parabola/index.html)
- [Focus of a Parabola: Definition, Formula, Examples](/content/math/geometry/focus-of-parabola/index.html)
- [Directrix of a Parabola: Definition, Equation, Examples](/content/math/geometry/directrix-of-parabola/index.html)
- [Ellipse - Equation, Formula, Properties, Graphing](/content/math/geometry/ellipse/index.html)
- [Foci of an Ellipse: Definition, Formula, Examples](/content/math/geometry/foci-of-ellipse/index.html)

## Transformations, Symmetry & Measurement
How figures move, flip, turn, and resize — plus the tools that measure angles and directions.

- [Geometric Transformations: Definition, Types, Examples](/content/math/geometry/transformations/index.html)
- [Symmetry in Geometry - Types, Definition, Examples](/content/math/geometry/symmetry/index.html)
- [Dilation in Geometry: Definition, Scale Factor, Examples](/content/math/geometry/dilation-geometry/index.html)
- [Scale Factor: Definition, Formula & Examples](/content/math/geometry/scale-factor/index.html)
- [Radians to Degrees — Conversion Table and Formula](/content/math/geometry/radians-to-degrees/index.html)
- [Angle Between Two Vectors: Formula & Examples](/content/math/geometry/angle-between-vectors/index.html)

## Why Geometry Matters
Geometry is the one school subject you can see out the window. It earns its place because it turns up everywhere abstract numbers alone can't reach:

- **Building and engineering.** A roof truss holds because its triangles can't deform — the one rigid polygon. Structural design is applied geometry.
- **Navigation and mapping.** GPS fixes your position by intersecting distance-spheres from satellites; the coordinate plane and the distance formula sit underneath every map app.
- **Computer graphics and games.** Every 3D scene is millions of triangles, rotated and scaled by transformation geometry, then projected onto a flat screen.
- **Design and manufacturing.** From a phone case to an aircraft wing, parts are specified as geometric solids with measured surface areas and volumes.

Geometry is also where many students first meet **proof** — the habit of arguing from a few accepted truths to a result that must follow. That reasoning skill outlasts any single formula.

## Key Takeaways
- **Geometry** studies points, lines, angles, shapes, and space — built from three foundations: the point, the line, and the plane.
- Its main branches are plane, solid, coordinate, and transformational geometry.
- This hub organizes every geometry topic into ten clusters, from foundations through conic sections, each linking to a full guide.
- The most reliable learning path runs foundations → angles → triangles → polygons and circles → solids → coordinate geometry.
- Beyond formulas, geometry teaches proof — reasoning from accepted truths to results that must follow.

## Frequently Asked Questions
**What is geometry in simple words?**  
Geometry is the part of mathematics that studies shapes, sizes, positions, and space — points, lines, angles, surfaces, and solids, and how they relate to each other.

**What are the main branches of geometry?**  
The main branches are plane (Euclidean) geometry, solid geometry, coordinate (analytic) geometry, and transformational geometry. Some courses also touch non-Euclidean geometry (spherical and hyperbolic).

**What are the basic concepts of geometry?**  
The three undefined building blocks are the point, the line, and the plane. From these come angles, shapes (triangles, quadrilaterals, polygons, circles), solids, and the theorems that connect them.

**What is the difference between plane and solid geometry?**  
Plane geometry deals with flat, two-dimensional figures (lines, angles, triangles, circles). Solid geometry deals with three-dimensional figures (prisms, pyramids, cylinders, spheres) and their volume and surface area.

**What grade do you start learning geometry?**  
Informal geometry — naming shapes and angles — begins in early primary grades. Formal geometry with proofs, theorems, and coordinate methods usually runs through middle and high school (roughly Grades 6–10).

**Is geometry hard?**  
Geometry feels different from arithmetic and algebra because it rewards visual reasoning and proof rather than calculation. Most students who struggle are missing a foundation term, not the ability — which is why this hub starts with points, lines, and planes.