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2.7 Prove Angle Pair Relationships   September 14, 2011




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HW pg.127 #3­6, 8­26 evens, 37­39                         1
2.7 Prove Angle Pair Relationships                         September 14, 2011




                    2.7 Prove Angle Pair Relationships

               Theorem 2.3: Right Angle Congruence Theorem
                          All right angles are congruent.
               Proof:
                      Given: <1 & <2 are right angles
                      Prove: <1 ≅ <2

                     Statements            Reasons
               1.   <1 & <2 are right <s   1. Given
               2.   m<1=90, m<2=90         2. Def. of Right Angle
               3.   m<1=m<2                3. Transitive Prop. of =
               4.   <1 ≅ <2                4. Def. of ≅ Angles




HW pg.127 #3­6, 8­26 evens, 37­39                                               2
2.7 Prove Angle Pair Relationships                     September 14, 2011




         Theorem 2.4: Congruent Supplements Theorem
                   If 2 angles are supplementary to the same angle,
                   (or ≅ to angles), then they are congruent.




HW pg.127 #3­6, 8­26 evens, 37­39                                           3
2.7 Prove Angle Pair Relationships                   September 14, 2011




   Theorem 2.5: Congruent Complements Theorem
                 If 2 angles are complementary to the same angle
                 (or ≅ to angles), then they are congruent.

                  5
              4         6


   If <4 & <5 are complementary and <6 & <5 are complementary,
   then <4 ≅ <6.


       Draw a diagram and write GIVEN and PROVE 
          statements for a proof of each case of the 
          Congruent Complements Theorem.




HW pg.127 #3­6, 8­26 evens, 37­39                                         4
2.7 Prove Angle Pair Relationships                            September 14, 2011




                                Postulate 12: Linear Pair Postulate
                                           If 2 angles form a linear pair,
                                           then they are supplementary

                     Theorem 2.6: Vertical Angles Congruence Theorem
                               Vertical angles are ≅.




HW pg.127 #3­6, 8­26 evens, 37­39                                                  5
2.7 Prove Angle Pair Relationships   September 14, 2011




HW pg.127 #3­6, 8­26 evens, 37­39                         6
2.7 Prove Angle Pair Relationships   September 14, 2011




    HW pg. 127
    #3­6,
    8­26 evens,
    37 & 39




HW pg.127 #3­6, 8­26 evens, 37­39                         7

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2.7 notes

  • 1. 2.7 Prove Angle Pair Relationships September 14, 2011 B E L L W O R K HW pg.127 #3­6, 8­26 evens, 37­39 1
  • 2. 2.7 Prove Angle Pair Relationships September 14, 2011 2.7 Prove Angle Pair Relationships Theorem 2.3: Right Angle Congruence Theorem All right angles are congruent. Proof: Given: <1 & <2 are right angles Prove: <1 ≅ <2 Statements Reasons 1. <1 & <2 are right <s 1. Given 2. m<1=90, m<2=90 2. Def. of Right Angle 3. m<1=m<2 3. Transitive Prop. of = 4. <1 ≅ <2 4. Def. of ≅ Angles HW pg.127 #3­6, 8­26 evens, 37­39 2
  • 3. 2.7 Prove Angle Pair Relationships September 14, 2011 Theorem 2.4: Congruent Supplements Theorem If 2 angles are supplementary to the same angle, (or ≅ to angles), then they are congruent. HW pg.127 #3­6, 8­26 evens, 37­39 3
  • 4. 2.7 Prove Angle Pair Relationships September 14, 2011 Theorem 2.5: Congruent Complements Theorem If 2 angles are complementary to the same angle (or ≅ to angles), then they are congruent. 5 4 6 If <4 & <5 are complementary and <6 & <5 are complementary, then <4 ≅ <6. Draw a diagram and write GIVEN and PROVE  statements for a proof of each case of the  Congruent Complements Theorem. HW pg.127 #3­6, 8­26 evens, 37­39 4
  • 5. 2.7 Prove Angle Pair Relationships September 14, 2011 Postulate 12: Linear Pair Postulate If 2 angles form a linear pair, then they are supplementary Theorem 2.6: Vertical Angles Congruence Theorem Vertical angles are ≅. HW pg.127 #3­6, 8­26 evens, 37­39 5
  • 6. 2.7 Prove Angle Pair Relationships September 14, 2011 HW pg.127 #3­6, 8­26 evens, 37­39 6
  • 7. 2.7 Prove Angle Pair Relationships September 14, 2011 HW pg. 127 #3­6, 8­26 evens, 37 & 39 HW pg.127 #3­6, 8­26 evens, 37­39 7