Triangle proportionality theorem

Use the applet below to discover the triangle proportionality theorem!
The segment DE // AC. Drag the point D and compare what you notice in the ratios.[br]What can you say about the [math]\Delta[/math]ABC and [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAOCAYAAAAmL5yKAAAAk0lEQVQ4T6XSwQkCMRCF4W9LESxDREuwBSuwCMvwYAe2oODZHqxAC/AgCxsIIZOIO6c5TP73B95g5gyd9wdc8IzueoAP7tj8AzhhiTUWkUXL4DolNy0iwJh+nvTHfR9ZRICUnr4eWtQAeXoChBY1QJnetCgBtfSmRQl449Eo1xa3vBc5YIXjD81+YZfuek3s8mYDvh15IA/tOoijAAAAAElFTkSuQmCC[/img]DBE ?

Information: Triangle proportionality theorem