Together with **Power Concepts**, triangle geometry solves obtaining *proportional means* through **theorems** called the **height** and **cateto**.

Before stating these theorems and deduce, recall some basic concepts of proportionality to understand what it is that we can solve with constructs derived from these geometric models.

### Fourth proportional

Given the mathematical relationship **x/a =b/c** call fourth proportional to the value of x, namely

x=a*b/c

### Third proportional

Given the mathematical relationship **x/a = a/b** called third proportional to the value of x, namely

x=a*a/b

### Proportional Media

Given the mathematical relationship **x/a=b/x** call mean proportional to the value of x, namely

x = square root of a * b

In the three cases defined, the ratio can be from models based on similarity and therefore obtained by applying the relationships **Thales theorem**.

## Triangle geometry

We can obtain a **triangle** hypotenuse using as a diameter of a circle, and as a point opposite corner of the same, and which defines a **arc able 90 grados** diameter on said.

If we get the **height h** the right-angled triangle from (vertex **A**) and determine its intersection **H** with the hypotenuse (**walk-up**) we can determine **three triangles similar rectangle**:

- ABC
- HAC
- HBA

Thales Applying these three triangles we obtain the following relations:

### Theorem catheter

The leg of a right triangle is the mean proportional between the hypotenuse and the projection of that leg on the hypotenuse.

**l*l=m*n**

### Height theorem

The height of a right triangle's hypotenuse measure mean proportional between the two segments that divides.

**l*l=m*n**