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Section 1.3: Collinearity, Betweenness, and Assumptions

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## Section 1.3: Collinearity, Betweenness, and Assumptions

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**C**A B C A B Collinearity • Collinear points are points that lie on the same line • Non-collinear points are points that do not lie on the same line Are A,B, and C collinear? Collinear Noncollinear**S**R S T R T Betweenness Betweenness occurs when one point is between two others, but… …all three points must be collinear Is S between R and T? Yes No, not collinear**Triangle Inequality**Any three points can be: • Collinear -One point between others • Noncollinear -Points determine a triangle**How to use the Triangle Inequality**• If we are given three segment lengths we can determine if they are collinear or make up a triangle. • If 2 measures add up to the third then they make up a line • If the sum of 2 measures is greater than the third then they make up a triangle**Example**• Determine if the following three segments make up a line or a triangle. • AB=17, BC=24, AC=39 • Add up AB and BC AB+BC=17+24=41 • Compare AB+BC to AC AB+BC>AC • Since the sum of two of the sides is greater than the third side the three sides make up a triangle.**What can we assume?**Straight lines and angles Collinearity Betweenness Relative positions What can’t we assume? Right angles Congruent angles Congruent segments Relative size of segments or angles Assumptions from diagrams**Can assume**Cannot assume Example D B E C A**Homework time!!**p. 20-22 1-14