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Warm Up

Warm Up. 1. 70 ï‚°. 2. Use a ruler to draw a large triangle. Measure the angles of the triangle. Make a conclusion about the sum of the measure of the angles of a triangle. 1.3 Collinearity, Betweeness, and Assumptions. Col line ar: points on the same line. Points ABC are collinear. A. B.

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Warm Up

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  1. Warm Up 1. 70 2. Use a ruler to draw a large triangle. Measure the angles of the triangle. Make a conclusion about the sum of the measure of the angles of a triangle.

  2. 1.3 Collinearity, Betweeness, and Assumptions 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. Triangle Inequality: For any three points, only two possibilities: Collinear: all points are on the same line. (2 Distances add up to the third distance) Noncollinear: 3 points determine a triangle Triangle Inequality: the sum of two sides is always greater than the third side. Why is this? Let’s take a ruler and measure to see if this is true!!!

  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. Example: 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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