maths.free › Geometry

Geometry

Shapes, measured. Give three sides and get every angle, the area and a drawn figure; give a radius and get a sphere you can spin. Coordinate geometry connects it all to algebra.

பாடங்கள்

Core Triangles Heron's formula, the law of cosines and classifying triangles. triangle 3 4 5 Introductory Pythagorean theorem a² + b² = c² in a right triangle, and where it comes from. hypotenuse of 3 and 4 Introductory Circles Circumference, area and the meaning of π. circle radius 2 Core Polygons Interior angles, apothem and area of regular polygons. hexagon side 2 Core Solids Volume and surface area of spheres, cylinders, cones, boxes and pyramids. volume of a sphere with radius 3 Core Coordinate geometry Distance, midpoint, slope and the equation of a line. line through (0,1) and (2,5) Introductory Euclid's axioms and the structure of proof Points, lines, the five postulates, and why geometry was the first axiomatic science. triangle 5 5 5 Core Congruent and similar triangles SSS, SAS, ASA congruence, and similarity by scaling. triangle 3 4 5 Core Circle theorems Inscribed angles, tangents, chords, and the angle in a semicircle. circle radius 5 Core Transformations: translation, rotation, reflection, dilation Rigid motions and scalings, and the matrices that perform them. inverse of [[0,-1],[1,0]] Core Solid geometry: prisms, pyramids, spheres Volumes, surface areas and cross-sections in three dimensions. volume of a cone with radius 3 height 4

Chapters from OpenStax Contemporary Mathematics

Every section of the book, condensed into a lesson with its own practice problems.

10. Geometry

Points, Lines, and PlanesAnglesPolygons, Perimeter, and CircumferenceTessellationsAreaVolume and Surface AreaRight Triangle Trigonometry

Symbols used here

\pi
pi
Ratio of a circle's circumference to its diameter, 3.14159…
\theta
theta
The usual name for an angle.
^\circ
degrees
1/360 of a full turn. 180° = π radians.
\sin,\ \cos,\ \tan
sine, cosine, tangent
Ratios of sides in a right triangle; coordinates on the unit circle.
\angle ABC,\ \triangle ABC
angle, triangle
The angle at B between BA and BC; the triangle with those vertices.
\parallel,\ \perp,\ \cong,\ \sim
parallel, perpendicular, congruent, similar
Never meet; meet at 90°; identical shape and size; same shape.

Questions people ask

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

மற்ற கிளைகள்

＋ Arithmetic𝑥 Algebra∿ Trigonometryƒ Precalculusσ Statistics & Probability⊢ Discrete Math & Logic∫ Calculus⊞ Linear Algebraℕ Number Theoryẏ Differential Equations∇ Multivariable Calculusε Real Analysis⋔ Combinatorics & Graph Theory∈ Set Theory & Logic𝔾 Abstract Algebra𝑃 Probability Theory≈ Numerical Methodsℂ Complex Analysis◎ Topologyμ Measure Theory‖·‖ Functional Analysisκ Differential Geometryπ₁ Algebraic Topology→ Category Theory∞ Frontiers