Question from Teresa:
I’m in Jacobs Geometry, Chapter 5, Lesson 2. In problems 32 and 33 looking at the figure I thought the answer was “given” for both of them. What the answer key says doesn’t seem to make sense with the question. Am I just misunderstanding the problem?
Answer from Dr. Callahan:
First – they are not “given” since there was nothing “given” in the problem or in the figure.
So instead he is asking us WHY these items can be determined – which is more definition.
I do realize this sounds silly – that a midpoint is possible because every line segment has one midpoint – but that is the idea he is after. He is trying to nail down that NOTHING can be said without backing it up with reason and fact.
You will find other instances of this in the book (and likely have already) but the trick is when you have a silly question – often it is either GIVEN (in which case look back at the problem and see if it is indeed given) or it is definition.
Hope this helps.