80 likes | 94 Views
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:.
E N D
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. Z Y X Z is between Y and X Y Z X X is not “between” Y and Z
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