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.
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...
There are some things that you can and can't assume from diagrams.
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
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 
Triangle Inequality
 Not just any three line segments can make a triangle.
On the left,  AB + BC = AC so it ends up being a straight line, not a triangle.
On the right, two of the segments cannot come to a point at the top because they are too short relative to the base.
SO... the sides of your triangle must fit the form
That's all we learned today
for Enjoyment and Challenge,  this is Olivia Miller

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