High School Geometry

What you can measure: length, mass, capacity, time, temperature.

A standard chunk you compare other things against — and why standards matter.

Convert any length, mass, volume, area, speed, or temperature — with the cancel-the-units trick.

Inch, foot, pound, gallon, acre, Fahrenheit — the system that runs the US, with a visual size chart.

kilo, mega, giga, milli, micro, nano — 14 prefixes that scale every metric unit.

mm, cm, m, km — and inches and feet.

mm, cm, m, km — base 10, easy to convert.

Inch, foot, yard, mile — and the conversions you really need.

Read clocks, count minutes, work with durations.

How many days in this month? When does the leap year fall?

Twelve months, names and origins — and how many days each one has.

Seven days, where the names come from, and how the modern week was set.

Sunrise to sunrise — and the 24 hours in between.

One trip around the sun — and why it's not exactly 365 days.

Spring, summer, autumn, winter — and the tilt of the Earth that drives them.

Seconds, minutes, hours, days — convert between any two.

Measuring elapsed time — for races, recipes and physics experiments.

Two ways to display the same time — read either at a glance.

Same shape, different size — corresponding sides scale together.

Same shape AND same size — SSS, SAS, ASA, AAS, RHS prove it.

The three angles always sum to 180°. Drag to convince yourself.

Centroid, circumcenter, incenter, orthocenter — four points every triangle hides.

Resize a rectangle and see area and perimeter follow.

Triangle 180°, quad 360°, pentagon 540° — sum grows by 180° per side.

Walk around a polygon — the turns always add to 360°.

Two sides always add to more than the third — or no triangle.

One 90° corner — and the home of Pythagoras and trig.

Three equal sides, three 60° angles — the most symmetric triangle.

Two equal sides — and the base angles are equal too.

All sides different — no symmetry.

The simplest right triangle in whole numbers — used since ancient Egypt.

Four right angles, opposite sides equal — the most familiar shape.

Three sides, two sides and an angle — build a triangle from any combination.

Spin a shape — does it look the same before a full turn?

Circle, triangle, square, polygon — names, sides, properties.

Three sides, four, five, six… and the angle each interior corner gets.

Cubes, spheres, cylinders — drag a dimension and watch volume grow.

(4/3)πr³ and 4πr² — Archimedes worked these out without calculus.

What's a cube in 4 dimensions? Or 5? You can almost picture it.

Polyhedra, prisms, pyramids, Platonic solids — Euler's V−E+F = 2.

Six squares, twelve edges, eight corners — the simplest 3D solid.

Every point the same distance from the center — the most efficient surface.

Two circles joined by a tube. Cans, pipes, drums.

A circle pulled to a point. Ice-cream, party hats, traffic markers.

A donut. One hole, but a surprising amount of geometry.

Same shape, top and bottom — connected by rectangles.

A polygon base, all sides meeting at one peak.

There are exactly five — tetrahedron, cube, octahedron, dodecahedron, icosahedron.

Unfold a solid into a flat net — a paper template you can cut and rebuild.

Four triangular faces — the simplest 3D solid.

Eight triangular faces — like two pyramids glued base to base.

Twelve pentagonal faces — one of the five Platonic solids.

Twenty triangular faces — the most spherical of the Platonic solids.

The waves trigonometry draws when you sweep an angle.

Triangles without right angles — two laws that solve them anyway.

sin, cos, tan and the right-triangle ratios behind every angle.

sin² + cos² = 1, and the family of equations that always hold.

The three things every other shape is built from.

Plot points, drag dots, watch (x, y) follow your finger.

Pythagoras turned into a coordinate formula.

The point exactly halfway between two given points.