What is a point? What is distance? And why do we need a reference frame to say where anything is?
Two points leave a line no choice. It has to go exactly there.
An angle is not a shape. It is a rotation. The number tells you how far.
Three is the minimum. Two points can't close space. Three can. And from that one fact, all of geometry grows.
One angle can dominate a triangle. The one that breaks 90° names the whole shape.
The biggest angle always faces the biggest side. You can feel it — and you cannot break it.
The square on the hypotenuse equals the sum of the squares on the other two sides. Always. For every right triangle that ever existed.
When are two triangles exactly the same shape and size? Four minimum tests — SSS, SAS, ASA, RHS — and why geometry needs them.
Four sides. The general case. A quadrilateral is not rigid — but one thing never changes no matter how you deform it.
Two pairs of parallel sides. A cascade of properties that nobody asked for — they just follow.
Explore the properties of four key quadrilaterals interactively — sides, angles, diagonals, and their hierarchy.