Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Geometric Proofs

37,796 views

Published on

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.

Published in: Education, Technology
  • Be the first to comment

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 />

×