Final answer:
In similar triangles, corresponding sides are proportional, which means lines AB and CD have the same slope due to their geometric similarity. This reflects the fact that in similar figures, angles and side ratios are preserved.
Step-by-step explanation:
The question provided pertains to similar triangles and the properties of their corresponding sides, specifically lines AB and CD. In similar triangles, corresponding sides are proportional, which means the slopes of the corresponding sides are equal because the triangles are geometrically similar. Thus, the true statement about lines AB and CD would be that they have the same slope. This is because the slope is a measure of the steepness of a line, and in similar triangles, the angles are preserved, which in turn preserves the slope of the lines.
When dealing with the algebra of straight lines, remember that the slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since similar triangles have sides that increase and decrease at the same rate, their slopes must be the same, regardless of their respective y-intercepts or the actual lengths of the sides.
To conclude, for similar triangles, statement c. 'the lines have the same slope' is accurate and reflects the geometric properties of these figures.