# Thales' Theorem

## Brief historical context

## Basic Definitions

## Property

## Analysis 1

Check the "Show / Hide Segment Measurements" box. Do segments AB, BC and CD have the same measure?

## Analysis 2

Check the "Show / Hide Segment Measurements" box. Move points E, F and D so that the parallel lines are equidistant from each other. Do segments AB, BC and CD have the same measure? Justify your answer (if you need help, check the "Show / Hide Triangle" box)

## Other property

## Analysis 3

The following structure shows the corresponding segment being divided into fewer parts. Explain what is wrong in the previous statement.

## Basic Concept

## Analysis 4

Move points A, A', D or D' and observe the ratios. Do they change?