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Collinearity, Betweeness, and Assumptions

Collinearity, Betweeness, and Assumptions. Lesson 1.3. Col line ar: points on the same line. Points ABC are collinear. A. B. C. Non-collinear: points that do not lie on the same line. B. A. You can connect AB, AC, or BC, but ABC does not form a line. C. Betweeness of Points:.

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Collinearity, Betweeness, and Assumptions

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  1. Collinearity, Betweeness, and Assumptions Lesson 1.3

  2. Collinear: points on the same line Points ABC are collinear A B C Non-collinear: points that do not lie on the same line B A You can connect AB, AC, or BC, but ABC does not form a line. C

  3. Betweeness of Points: To have betweeness of points, all points must be on the same line. Z Y X Z is between Y and X Y Z X X is not “between” Y and Z

  4. Two possibilities with 3 points Collinear: all points are on the same line. Triangle : makes a triangle. Triangle Inequality The sum of two side lengths is always greater than the third side.

  5. Assumptions from diagrams: Can assume: Straight lines Straight angles Collinear points Betweenness of points Relative position of points

  6. Can’t Assume! Right angles Congruent segments Congruent angles Relative size of angles Relative size of segments

  7. Example: B D A C E Assume: AD and BE straight lines C, D, E non-collinear C is between B and E E is to the right of A

  8. B D A C Can’t Assume: <BAC is a right angle CD = DE <B = <E <CDE is obtuse BC is longer than CE E

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