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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.

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    Can you add the image to the question? I would be happy to provide a heuristic answer. – 2017-02-20
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    @TheCount The proof I referred to is hyperlinked under the word "internet". It requires right at the outset that a perpendicular line be drawn connecting one vertex of the triangle to one of its sides. I just wonder whether it is always possible to draw such a line inside a triangle, regardless of the lenghts of the sides – 2017-02-20
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    the longest edge is always 'inside' for the perpendicular. – 2017-02-20
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    @NickD. I think you misunderstood. you can always draw a perpendicular inside, just not necessarily from *every* vertex. – 2017-02-20
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    You're right, I didn't read that carefully enough! Thanks. – 2017-02-20

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