With an understanding of distance, we can now define lines and circles. Once we define them, we can define angles and triangles. After that, we get all sorts of interesting figures to ponder.
Every portion of a line is a straight path (line segment). Straight line kind of redundant but not entirely. That is any two points on a line have the property that the shortest path between them lies on the line.
All points a fixed distance from a given center point. This can be done by taking a line segment and sweeping it out with one point fixed.
Circumference, area
Angles represent two lines meeting. To be specific, pick the two halves of the lines (rays) which will represent the sides of the angle. The intersection point is called vertex.
Given two points on a circle, measure distance along the circle. Divide by circumference. This gives a decimal representation of the measure of the angle. It is truly unitless.
One can get customary measures by multiplying by whatever a full rotation should measure to be; 360 for degrees, 2pi for radians
Three points, three line segments joining them. Defines a triangle.
Angles add up to a straight angle.
right triangles
Pythagorean Theorem
Area?
A quick intro to polygons? Followed by dividing up a circle with n points and computing the circumference/area? maybe in proofs? ???