So, I've come across this proof for the ratio of corresponding sides of similar triangles on the internet, but the proof requires that we draw a perpendicular line (an altitude) inside the triangle.
It might seem a silly question, but how can I be sure it is always possible to draw a perpendicular line connecting one vertex of any triangle to one of its sides? In other words, how can I show that every triangle has at least one altitude which lies within the triangle? Thanks.