What is the inverse theorem of parallel lines?

Description: Three straight lines cut two straight lines. If the corresponding line segments cut are proportional, the three lines are parallel.

Geometric language: I don't have a drawing tool installed on this computer. You can draw:

Draw three straight lines, A, B a, B, c d, which are roughly horizontal.

Draw two more straight lines, m and n in figure 8.

Let a and m intersect at a, and n intersect at d,

B and m intersect at b, n intersects at e,

C and m intersect at c, n intersects at f,

If AB :BC = DE :EF, then A is parallel to B and C is parallel.

Or if AB :AC = DE :DF, then a is parallel to b and c is parallel.

Or it can be written in other forms. It's in the book.

Of course, graphics can also be drawn in various ways.

If AB :BC = DE :EF, then A is parallel to B and C is parallel.

In this regard, I often think that if the top left: bottom left = top right: bottom right, the three lines are parallel.

Or if AB :AC = DE :DF, then a is parallel to b and c is parallel.

In this regard, it is often remembered that if top left: left all = top right: right all, the three lines are parallel.

Also: if bottomleft: leftall = bottomright: rightall, then these three lines are parallel.