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

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

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

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

For any 3 points there are only 2 possibilities: 1.They are collinear (one point is between the other two and two of the distances add up to the 3 rd ) 2.They are noncollinear (the 3 points determine a triangle) Triangle Inequality 5.5 A 12.5 B C A B C

Notice in this triangle, > 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” Triangle Inequality A B C

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! Assumptions You should AssumeYou should NOT Assume *Straight lines and angles *Collinearity of points *Betweenness of points *Relative positions of points *Right angles *Congruent segments *Congruent angles *Relative sizes of segments and angles

Lesson 1.3 Worksheet Homework