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.


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