Hello again, norifurippu!

So we know the 2 triangles are similar only because m1 and m2 are parallel?

Is there anything else we need to know 2 triangles are similar? Here's a more complete explanation . . .

Code:

B
o
/ *
m1 / *
/ *
A o - - - - - - - - - o - - - - - - - - - - - - - - o E
C * /
* /
* / m2
* /
* /
o
D

Since $\displaystyle m1 \parallel m2\!:\;\;\angle A \,=\,\angle E $ . (alternate-interior angles)

Also: .$\displaystyle \angle BCA \,=\,\angle DCE$ . (vertical angles)

Hence: .$\displaystyle \angle B \,=\,\angle D$

Therefore: .$\displaystyle \Delta ABC \:\sim\: \Delta CDE$ . (a.a.a.)