Locate a closed angle in the triangle.
Place a finger on that point; call it Point A. Follow the line from Point A to the next angle. If there's a closed angle, or if there's a closed point, then this is your first line segment. If there's an arrow, then this is a ray. For the sake of practice, let's say this second angle is a closed angle, and this will be called Point B.
Drag your finger from Point B to the last remaining angle; call that Point C. Finish the test by dragging your finger from Point C to Point A. As long as the line is connected by two points, then you can count it as a line segment.
Repeat for the second triangle. If the triangles are connected by the same horizontal line, but are separated by Point C, then these are technically two line segments. The key is to go from each connected point to the next point.