Geometry Chapter 2 + Ch 1/2 Postulates/Theorems/Properties of Equality

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Minhs2
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171337
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Geometry Chapter 2 + Ch 1/2 Postulates/Theorems/Properties of Equality
Updated:
2012-09-23 23:20:33
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Geometry chapter minhs2 holt california postulate theorems
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CA Holt Ch2 Vocab Words and Ch 1 and 2 postulates and theorems.
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  1. biconditional statement
    A statement that can be written in the form "p if and only if q."
  2. conclusion
    The part of a conditional statement following the word then.
  3. conditional statement
    A statement that can be written in the form "if p, then q," where p is the hypothesis and q is the conclusion.
  4. conjecture
    A statement that is believed to be true.
  5. contrapositive
    The statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement.
  6. converse
    The statement formed by exchanging the hypothesis and conclusion of a conditional statement.
  7. counterexample
    An example that proves that a conjecture or statement is false.
  8. deductive reasoning
    The process of using logic to draw conclusions.
  9. definition
    A statement that describes a mathematical object and can be written as a true biconditional statement.
  10. flowchart proof
    A style of proof that uses boxes and arrows to show the structure of the proof.
  11. hypothesis
    The part of a conditional statement that goes after the word if.
  12. inductive reasoning
    The process of reasoning that a rule or statement is true because specific cases are true.
  13. inverse
    The statement formed by negating the hypothesis and conclusion of a conditional statement.
  14. logically equivalent statements
    Statements that have the same truth value.
  15. negation
    The negation of statement p is "not p."
  16. paragraph proof
    A style of proof in which the statements and reasons are presented in paragraph form.
  17. polygon
    A closed plane figure formed by three or more segments so that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear.
  18. proof
    An argument that uses logic to show that a conclusion is true.
  19. quadrilateral
    A four-sided polygon.
  20. theorem
    A statement that has been proven.
  21. triangle
    A three-sided polygon.
  22. truth value
    A statement can have a truth value of true or false.
  23. two-column proof
    A style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.
  24. 2 points postulate
    Through any 2 points there is exactly one line.
  25. 3 points postulate
    Through any three noncollinear points there is exactly one plane containing them.
  26. 2 Points and A Line Postulate
    If two points lie in a plane, then the line containing those points lies in the plane.
  27. Intersecting Lines Postulate
    If two lines intersect, then they intersect in exactly one point.
  28. Intersecting Planes Postulate
    If two planes intersect, then they intersect in exactly one line.
  29. Ruler Postulate
    The points on a line can be put into a one-to-one correspondence with all real numbers.
  30. Segment Addition Postulate
    If B is between A and C, then AB plus BC equals AC.
  31. Protractor Postulate
    Given AB and a point O on AB, all rays that can be drawn from O can be put into a one-to-one correspondence with the real numbers from 0 to 180.
  32. Angle Addition Postulate
    If D is in the interior of angle ABC, then the measure of angle ABD plus measure of angle DBC equals measure of angle ABC.
  33. Pythagorean Theorem
    If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
  34. Linear Pair Theorem
    If two angles form a linear pair, then they are supplementary.
  35. Congruent Supplements
    If two angles are supplementary to the same angle or to two congruent angles, then the two angles are congruent.
  36. Right Angle Congruence Theorem
    If an angle is a right angle then it is congruent to other right angles.
  37. Congruent Complements
    If two angles are complementary to the same angle or to two congruent angles, then the two angles are congruent.
  38. Common Segments Theorem
    Given you have collinear points A, B, C, and D arranged as given, if  segment AB is congruent to segment CD, then segment AC is congruent to segment BD.
  39. Vertical Angles Theorem
    If 2 angles are vertical angles, then they are congruent.
  40. Congruent and Supplemental Angles Theorem
    If two congruent angles are supplementary, then each angle is a right angle.
  41. Addition Property of Equality
    If A equals B, then A plus C equals B plus C
  42. Subtraction Property of Equality
    If A equals B, then A minus C equals B minus C
  43. Multiplication Property of Equality
    If A equals B, then A  C times B times C
  44. Division Property of Equality
    If A equals B and C is not equal to 0, then A divided by C equals B divided by C
  45. Reflexive Property of Equality
    A equals A
  46. Symmetric Property of Equality
    If A equals B, then B equals A
  47. Transitive Property of Equality
    If A equals B and B equals C, them A equals C
  48. Substitution Property of Equality
    If A equals to B, then B can be substituted for A in any expression
  49. Reflexive Property of Congruence
    Figure A is congruent to figure A
  50. Symmetric Property of Congruence
    If figure A is congruent to figure B, then figure B is congruent to figure A
  51. Transitive Property of Congruence
    If figure A is congruent to figure B and figure B is congruent to figure C, then figure A is congruent to figure C
  52. Law of Detachment
    If p then q is a true statement, and p is true, then q is true
  53. Law of Syllogism
    If p then q and q then r are true statements, then p then r is a true statement

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