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1.3 Segments and their measures Schiewe 2004-5 Review of 1.1 and 1.2 What is a conjecture? An unproven statement based on observation. What do we call something which proves a conjecture wrong? A counterexample Review cont. Define the following symbols. AB, CD, GH, HG Line AB Line segment CD Ray GH, G is the endpoint Ray HG, H is the endpoint Defining POSTULATE 1. 2. 3. 4. Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument: “the postulate that there is little moral difference between the superpowers” (Henry A. Kissinger). A fundamental element; a basic principle. Mathematics. An axiom. A requirement; a prerequisite. Now, Let’s define AXIOM Axiom L. axioma, Gr. ? that which is thought worthy, that which is assumed, a basis of demonstration, a principle a self-evident truth An established rule, principle, or law. What’s up with 2 slides of definitions – Judas Priest… Postulates and axioms are fun-Dmental rules. Like 1 comes before 2… or geometry is so fun… or … DISTANCE is always positive. If you go from 2 to 5 or from 7 to 4, you traveled a DISTANCE of 3 units, DUHHHHHHHHHH. (understood) Hey a postulate!!!!! New Symbol – exciting stuff We know how to denote line, line segment, and ray. Length of segment AB is easier than all of these. It is simply… AB, yes, that is right, AB No line on top, no nothing! Just the two points A and B written next to each other. AB Simply AB The word between between “Between” can only happen when all 3 points are collinear. So, – A B C B is between A and C because… A, B, and C are collinear! Definitely, NOT between A B C Segment addition postulate If B is between A and C, then AB + BC = AC If AB + BC = AC, then B is between A and C. Finding distance Find the horizontal distance Square that number Find the vertical distance Square that number, too. Add those two squared numbers Take the square root, and then you have DISTANCE Distance between (1,6) and (4,10) Horizontal distance = ? 4-1 = 3 Square that… 3x3 = 9 Vertical distance = ? 10– 6 = 4 Square that… 4x4 = 16 Add the two squared numbers. 9+16 = 25, square root of 25 = 5. Good d = 5