Combining shapes via a common line

I have an Inkscape drawing with several separate shapes on it, transferred from another application. Each of the shapes is a closed sequence of line segments, not necessarily convex. I know that there are two shapes in the drawing each of which contains a line segment of a certain length. E.g., the shapes might be ABCDEA and VWXYV, with line BC the same length as VY. The two segments BC and VY might be in any position or orientation relative to each other on the drawing.

I want to create a new drawing which combines the two shapes by superimposing the common line. In CorelDraw this would be easy: since it’s possible to make line ends “magnetic”, I could first lock B to V by pulling one shape towards the other, then lock C to Y by an appropriate rotation around B. Does Inkscape have the same capability? I don’t want to distort either of the component shapes.

I just discovered Inkscape and this operation is one I will use a lot. I’m sure this is a beginner question, but I haven’t been able to find it in the tutorials. Thank you kindly for your help!