In two similar triangles their median, height, angle bisector and perpendicular bisector (upon middle of a side) are all scaled like perimeters (with same similarity ratio).
But can I say so for any line within two triangles?
a) line ending on the sides of a triangle
b) line strictly inside triangle (not touching the sides)
Say, the line from a vertex divides the side (opposite the vertex) as 1 : 3 in both triangles. Etc.