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Lesson 1.3 Collinearity, Betweenness, and Assumptions

Lesson 1.3 Collinearity, Betweenness, and Assumptions. Objective: Recognize collinear, and non-collinear points, recognize when a point is between two others, recognize that each side of a triangle is shorter than the sum of the other two sides, and correctly interpret geometric diagrams.

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Lesson 1.3 Collinearity, Betweenness, and Assumptions

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  1. Lesson 1.3 Collinearity, Betweenness, and Assumptions Objective: Recognize collinear, and non-collinear points, recognize when a point is between two others, recognize that each side of a triangle is shorter than the sum of the other two sides, and correctly interpret geometric diagrams

  2. Definitions… Def. Points that lie on the same line are called collinear. Def. Points that do not lie on the same line are called noncollinear. P U H A S N Collinear Noncollinear

  3. Example #1 Name as many sets of points as you can that are collinear and noncollinear M P O X Y T R S

  4. Definitions… In order for us to say that a point is between two other points, all three points MUST be collinear. U P A H S N P is NOT between H and S A is between N and U

  5. Triangle Inequality • For any 3 points there are only 2 possibilities: • They are collinear (one point is between the other two and two of the distances add up to the 3rd) • They are noncollinear (the 3 points determine a triangle) C 5.5 B 12.5 A 18 B 14 11 C A 24

  6. Triangle Inequality Notice in this triangle, 14 + 11 > 24. This is extra super important! “The sum of the lengths of any 2 sides of a triangle is always greater than the length of the third” B 14 11 C A 24

  7. Assumptions When given a diagram, sometimes we need to assume certain information, but you know what they say about assuming…. There are do’s and don’ts!

  8. Homework Lesson 1.3 Worksheet

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