"1 3 Collinearity Betweenness Assumptions"
Collinearity, Betweenness, & Assumptions Geometry 1.3 Collinear Points: Points on the same line. A B C A, B, and C are COLLINEAR points. Non-Collinear Points: Points not on the same line. A, B, and C are Non-COLLINEAR B points. A C Betweenness: Points must lie on the same line and AB + BC = AC. Y A B C Z “B is between A and C” X Symbols: A-B-C “Y is not between X and Z” because the points are not on the same line. Triangle Inequality: The sum of two sides of a triangle must always be greater than the third side. 3 B 8 AB = 3 BC = 8 AC = 11 } 3 Triangle can’t exist! 8 A C A B C Triangle Inequality: The sum of two sides of a triangle must always be greater than the third side. 5+7>x 5 7 12 > x AND 5+x>7 X x>2 AND So, 2 < x < 12 7+x>5 x < -2 Assumptions From A Diagram. Can Assume: 1. Straight Lines and Angles 2. Collinearity of Points 3. Betweenness of Points 4. Relative Position of Points Assumptions From A Diagram. Can Not Assume: 1. Right Angles 2. Congruent Segments 3. Congruent Angles 4. Size of An Angle