One of my students, Lucy, was having trouble understanding when it was not possible for three line segments to create a triangle. I decided the best way to help her was to give her a hands-on demonstration of why this is true, so that she could tell me why it was not possible to create a triangle with three given line segments.
I cut out three thin strips of paper. One of the strips was longer than both of the other strips combined. I asked Lucy if she could create a triangle with the three strips of paper I gave her. She was unable to do so, because the shorter strips of paper could not touch to form a third vertex when they were attached to the ends of the longer strip of paper. Lucy explained that the two strips were not long enough to make a triangle.
I created another three strips of paper. This time the long strip was the same length as both of the other strips combined. I showed her that in this case, thre three strips could make a straight line, but not a triangle.
Her face lit up as it all made sense to her. She told me, "Oh, so the two smaller lines have to be longer than the larger line!" That was what I had tried to explain to her - but it didn't make sense to her until she saw it.
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