In triangle ABC, if which of the following must be true?
I.
II.
III.
Why is it only I and III? How can I both prove these are correct and disprove II?
I. If the triangle was equilateral, then all 3 angles would be
Hence, if the triangle has a largest angle, it is greater than
while all angles must be less than so that they can sum to
III. If one angle is greater than than another must be less than
This is because the two remaining angles sum to less than
and if they were equal, they'd both be less than
II. If and then contradicts the statement.
Hmm but how come that would be 2's explanation (the triangle inquality theorem would fail wouldn't it?) Also, I still don't understand why angle a could be 179 (since that value would fit the bounds given--again the triangle inequality theorem would fail for angles b and c.) Maybe if we took some concrete examples? I still don't see it yet