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

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