## Thursday, September 9, 2010

### Section 1.3: Collinearity, Betweenness, and Assumptions

Points that lie on the same line are called collinear.
Points that do not lie on the same line are called noncollinear.
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When you say a point is between two other points,  the points must be collinear.
On the left, points A, B, and C are collinear;
point B is between points A and C.
On the right, A, B, and C are not collinear;
so point B is not between points A and C...
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There are some things that you can and can't assume from diagrams.
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You should assume:
straight lines and angles... if a line looks straight, it is
the collinearity/ betweenness of points... if they look collinear, they are
the relative positions of points... if A appears to the right of B, then it is
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You should not assume:
right angles... if it looks like a right angle, it doesn't mean it is
congruent segments/angles... if they look the same, it doesn't mean they are
relative sizes of segments/ angles... if one looks bigger, it doesn't mean it is
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Triangle Inequality
Not just any three line segments can make a triangle.
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On the left,  AB + BC = AC so it ends up being a straight line, not a triangle.
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On the right, two of the segments cannot come to a point at the top because they are too short relative to the base.
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SO... the sides of your triangle must fit the form
AB+BC>AC
(AB+AC>BC
AC+BC>AB)
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That's all we learned today
for Enjoyment and Challenge,  this is Olivia Miller