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

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 X Z X is not “between” Y and Z

For any three points, only 2 possibilities: 1.Collinear: all points are on the same line. (2 Distances add up to the third distance) 2.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!!!

Assumptions from diagrams: Can assume: 1.Straight lines 2.Straight angles 3.Collinear points 4.Betweenness of points 5.Relative position of points

Can’t Assume! 1.Right angles 2.Congruent segments 3.Congruent angles 4.Relative size of angles 5.Relative size of segments

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

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