A discussion of Thales Theorem is here.
The figures below can be dragged dynamically so that both cases of positive and negative ratio can be observed.
The first figure was constructed using a line through C parallel to AB; the line can be changed by dragging C. The second was constructed by scaling by the ratio OR/OP which can be changed by dragging R.
Thales Constructed by Parallel Line. Drag C.
Thales Construct by Ratio. Drag R.