SOLUTION: State whether the sentence is Always, never, or sometimes The three altitudes of a triangle intersect at a vertex of the triangle

Question 520147: State whether the sentence is Always, never, or sometimes
The three altitudes of a triangle intersect at a vertex of the triangle
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Sometimes, because we can find cases where the statement is true and other cases where the statement is not true.

The statement is true if the triangle is a right triangle (try this for yourself and you'll see). The statement is not true if the triangle is an equilateral triangle (since the orthocenter will be in the middle). Hence the statement is "sometimes" true.

Note that we did not have to find all cases where the statement is or is not true. We only need one counterexample to eliminate the choices "always" and "never."
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