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3.2 Postulates, Definitions, and properties Postulate - a STATEMENT that is accepted without PROOF . Sketch the following: If pt. Y is between pts. X and Z, then X, Y, and Z are collinear and XY + YZ = XZ Definition- the meaning of a word. An obtuse angle is an angle that measures between 90°and 180°. Biconditional- a statement that contains the words IF and ONLY IF . It is equivalent to writing a conditional and it’s converse, if p then q, and if q then p. Property Example REFLEXIVE PROPERTY a=a Symmetric Property: If a = b , then b = a . , and Transitive Property: If a=b, and b=c, then a=c If and , then Substitution Property: If a = b , then a can be substituted for b (and b for a ). If and , then Addition Property: If a=b, then a+c=b+c If PQ=RS, then PQ+QR=RS+QR SUBTRACTION PROPERTY: If AC = BD , then AC BC = BD BC .
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If a=b, then a-c=b-c For Exercises 1–4, tell whether each statement is a postulate or a definition. Tell which diagram, (a) or (b), illustrates the situation.
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Unformatted text preview: 1. Points that are on the same line are collinear. 2. Three noncollinear points determine a plane. 3. Coplanar points are points that lie in the same plane. 4. Two points determine a line. For Exercises 5–8, tell whether each argument uses inductive or deductive reasoning. 5. The rain stopped, and the sun came out. Next, a rainbow will appear. 6. Jose put $25 into savings each week for 10 weeks. Therefore, Jose has put $250 into savings during this period. 7. Quadrilateral RTGL is a rectangle. All rectangles are parallelograms. So quadrilateral RTGL is a parallelogram. 8. The first three numbers of a pattern are 1, 2, 4. So, the next number is 7. Identify the property that makes each statement true. 9. Tell which of the two arguments is invalid. Explain why it is invalid. 13. (a) Vertical angles are congruent. . Therefore, and are vertical angles. (b) Vertical angles are congruent. and are vertical angles. Therefore, ....
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This note was uploaded on 07/19/2010 for the course MATH Geo100 taught by Professor Any during the Spring '10 term at École Normale Supérieure.

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3_2 notes completed - 1. Points that are on the same line...

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