Collinearity, Betweeness, and Assumptions Lesson 1.3

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

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

Triangle Inequality 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.

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

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

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

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