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Geometric Proofs


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This slideshow helps introduce geometric proofs. It gives key elements and types of reasons then gives several different types of proofs. Toward the end of the slideshow- the two column proof's statements and reasons are scrambled and the students are responsible for unscrambling the proof. There are also some fill in the blank for students to complete.

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Geometric Proofs

  1. 1. Geometric Proofs<br />27 October 2009<br />
  2. 2. Geometric Proofs<br />TWO COLUMN PROOFS<br />FIVE KEY ELEMENTS <br />Given<br />Diagrams<br />Prove<br />Statements<br />Reasons<br />
  3. 3. Reasons<br />Given Information<br />Definitions<br />Postulates<br />PROPERTIES<br />Theorems<br />
  4. 4. Given: <br />PROVE:<br /> STATEMENTS Reasons <br />1. <br />1. Given<br />2. Definition of supplementary angles<br />2. <br />3. Substitution Property<br />3. <br />4. <br />4. Subtraction Property<br />5. <br />5. Definition of Congruent Angles<br />
  5. 5. Given: <br />Prove: <br />B<br />1<br />2<br />3<br />A<br />C<br />
  6. 6. Statements Reasons<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />7.<br />8.<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />7.<br />8.<br />Given<br />Definition of Right Angle<br />Angle Addition Postulate<br />Substitution Property (Steps 2 and 3)<br />Given<br />Definition of Congruent Angles<br />Substitution Property (Step 4 and 6)<br />Definitions of Complementary Angles<br />
  7. 7. Given: <br />Prove: <br />A<br />X<br />45˚<br />B<br />C<br />
  8. 8. QUIZ<br />What is always the first step of a proof?<br />Name 5 key elements of a proof.<br />Name 5 types of reasons one can use during a proof.<br />Measures __________: Angles and Segments are ______________.<br />What is the last statement in a proof?<br />
  9. 9. Statements Reasons<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />7.<br />8.<br />9.<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />7.<br />8.<br />9.<br />Given<br />Definitions of Angle Bisector<br />Definitions of Congruent Angles<br />Given<br />Substitution Property<br />Angle Addition Postulate<br />Substitution Property<br />Simplify<br />Definition of Right Angle<br />
  10. 10. Given: <br />Prove: <br />C<br />D<br />A<br />B<br />E<br />
  11. 11. Statements Reasons<br />1.<br />2.<br />3.<br />4.<br />5.<br />1.<br />2.<br />3.<br />4.<br />5.<br />Given<br />Given<br />Given<br />Definition of Midpoint<br />ASA (Steps 1, 4, 2)<br />
  12. 12. Given:<br />Prove:<br />1<br />A<br />D<br />2<br />B<br />C<br />
  13. 13. Statements Reasons<br />Converse of the Consecutive Interior Angles Theorem<br />Given<br />Perpendicular Transversal Theorem<br />Given<br />Definition of Supplementary Angles<br />
  14. 14. Given:<br />Prove:<br />B<br />D<br />1<br />2<br />3<br />4<br />A<br />E<br />C<br />
  15. 15. Statements Reasons<br />Substitution Property<br />5.<br />6.<br />Given<br />3.<br />2.<br />Corresponding Angles Postulate<br />2.<br />3.<br />Given<br />1.<br />1.<br />Substitution Property<br />4.<br />5.<br />Converse of Corresponding Angles Postulate<br />6.<br />4.<br />
  16. 16. Given:<br />Prove:<br />Z<br />Y<br />X<br />W<br />
  17. 17. Statements Reasons<br />1.<br />2.<br />3.<br />4.<br />5.<br />1.<br />2.<br />3.<br />4.<br />5.<br />Segment Addition Postulate<br />Substitution Property<br />
  18. 18. Given:<br />Prove:<br />L<br />M<br />4<br />5<br />O<br />N<br />
  19. 19. Statements Reasons<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />1.<br />2.<br />3.<br />4.<br />5.<br />6.<br />Definition of Right Angle<br />Substitution Property<br />