Synthetic geometry

Synthetic geometry is a fancy way of saying that we study shapes and their properties without using any numbers or measurements. Imagine that you have a bunch of pencils, erasers, and paper. You can use those tools to draw shapes and then figure out what those shapes can do without measuring them with a ruler.

For example, think about a triangle. You can draw a triangle on a piece of paper using pencils and then look at it. You might notice that all three sides of the triangle are straight lines and that the triangle has three corners or vertices. You can also draw a perpendicular line from one of the vertices to one of the sides of the triangle and see that it creates a right angle. This is a property of all right triangles that you can understand just by looking at them without measuring anything.

Synthetic geometry is important because it allows us to study abstract mathematical ideas without relying on numerical values. It can help us understand the relationships between shapes, the rules that they follow, and the patterns that they create. In other words, you don't need fancy tools or complicated formulas to learn about geometry - all you need is a pencil and some paper!