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Warm Up Assume the first two statements are true by chrisandersen

VIEWS: 10 PAGES: 11

									    Warm Up
    Assume the first two statements are true. Tell whether the third statement is
    valid or not valid. If it is valid, state which law ­ Law of Syllogism or Law of
    Detachment ­ that you used.

    1. (1)If you are a GHS student, then you like early release days.
        (2) Jim likes early release days.
        (3) Jim is a GHS student.


    2. (1) If GHS will win the football game tonight, then the fans will be very excited.
        (2)  GHS will win the football game tonight.
        (3)  The fans will be very excited.




Title: 2.4­6 (1 of 11)
                                   Page 112
   Page        99
                                        1.     <QRS, Transitive
   1.      Symmetric Property           3.     <A       19.   <1=<3, <2=<4
   4.      C                            4.     No       22.   <ABC = <DBF
   8.      D                            5.     Yes
   10.     m<B = m<A                                          <ABD = <CBF
                                        6.     No
   11.     BC = EF                      7.     No       27.   W = 10
                                        8.     Yes            X = 40
                                        9.     Yes
                                        12.    28
   Page 104                             13.    31
                                        14.    34
   1.    CD, AB                         15.    158
   22.   C                              16.    59
   36.   No                             17.    61
   37.   If the car is in the garage, then Mark is home
   38.   If Mark is home, then the car is in the garage.
   39.   If the car is not in the garage, then Mark is not 
   home.
   40.   If Mark is not home, then the car is not in the 
   garage.

Title: Sep 16­6:48 AM (2 of 11)
 2.4­6

 Algebra Properties of Equality:

 Addition Property ­ If a = b, then a + c = b + c.
 Subtraction Property ­ If a = b, then a ­ c = b ­ c.
 Multiplication Property ­ If a = b, then ac = bc.
 Division Property ­ If a = b and c ≠ 0, then a/c = b/c.
 Reflexive Property ­ For any real number a, a =a.
 Symmetric Property ­ If a = b, then b = a.
 Transitive Property ­ If a = b and b = c, then a = c.
 Substitution Property ­ If a = b, then a can be substituted for b in any equation or
                             expression.
 Distributive Property ­ a (b + c) = ab + ac




Title: 2 (3 of 11)
   The properties of equality can be applied to geometry also with segments
   and angles.

                           Segment Length                Angle Measure
   Reflexive          For any segment AB,           For any angle A,
                      AB = AB or AB ≅ AB.           m<A = m<A or <A ≅<A.

   Symmetric         If AB = CD, then CD = AB.      If m<A = m<B, then m<B = m<A.
                               OR                                  OR
                     IF AB ≅ CD, then CD ≅ AB.      If <A ≅<B, then <B ≅ <A.


 Transitive          If AB = CD and CD = EF,         If m<A = m<B and m<B = m<C,
                                    then AB = EF.              then m<A = m<C.
                                    OR                              OR
                     If AB ≅ CD and CD ≅ EF,         If <A ≅ <B and <B ≅ <C,
                                    then AB ≅ EF.              then <A ≅ <C.


Title: 3 (4 of 11)
    State the property ­ reflexive, symmetric, or 
    transitive that is used in the following 
    statements.

    1.  If MN = KP, then KP = MN.

    2. If <L ≅ <F and <F ≅ <X, then <L ≅ <X.

    3.  WR ≅ WR

    Using the given property, complete the 
    statement.

    4.  Transitive Property:  If ML ≅ _____ and 
              XY ≅ RP, then _____ ≅ RP.
    5.  Reflexive Property:  m<JKL = ______.

    6.  Symmetric Property:  If m<G = m<D, 
                        then __________.

Title: 4 (5 of 11)
   Linear Pair Postulate:  If two angles form a linear 
   pair, then they are supplementary.

                         1       2        If <1 and <2 are a linear pair,
                                          then m<1 + m<2 = 180o.


    Theorem - a true statement that follows as a result of other
    true statements. All theorems must be proved.


    Theorem 2.3: Right angles congruence theorem ­ If
    two angles are right, then they are congruent.

                     1
                                     If <1 and <2 are right angles, 
                             2                then <1 ≅ <2.



    Theorem 2.6: Vertical angle theorem
     If two angles are vertical, then they are congruent.


                                        If <1 and <2 are vertical angles,
                         1       2               then <1 ≅ <2.




Title: 5 (6 of 11)
Theorem 2.4: Congruent supplements theorem
If two angles are supplementary to the same angle, then the
two angles are congruent.

     If m<1 + m<2 = 180o and m<2 + m<3 = 180o,
                   then <1≅<3.

Theorem 2.5: Congruent complements theorem
If two angles are complementary to the same angle, then the
two angles are congruent.

     If m<4 + m<2 = 90o and m<2 + m<5 = 90o,
                   then <4≅<5.
                      Do
                         e
                     Su s tha
                       ppo     tr
                           se      e
                              m< ally w
                                 2=        o !
                                     30 dork? s
                                       ito. e 50    o
                                S ure         =1
                                         m<1        .
                                   use         m<3
                              Beca o does
                                and
                                     s          akes
                                      , th at m
                                                   d
                                 Also = 60oan
                                                      .
                                    m <4        o too
                                           = 60
                                     m<5




Title: 6 (7 of 11)
               What can you conclude using the postulate or theorems we've
               just talked about? Which postulate or theorem did you use?

               1.    If <Y and <Z are vertical angles, then __________.

               2.    If <W and <N are supplementary and <N and <S are
                     supplementary, then __________.

               3.    <P and <Q are both complementary to <H. Therefore,
                     __________.

               4.    <T and <M are right angles. Therefore, __________.

               5.    <GHI and <IHK are a linear pair. Therefore,
                     ____________________.


Title: 7 (8 of 11)
                             Pairs of Angles

                  Adjacent
                                      Congruent 

                                              Vertical




  Determine where each of the following pairs 
  of angles should go in the Venn Diagram.
     1.                          2.
              1                               7
                     2 45o                        8



     3.                         4.
                         5
                                      3
                                          4
                     6


Title: 8 (9 of 11)
                               Pairs of Angles

                      Adjacent
                                         Congruent 

                 <11,<12                       Vertical
                              <5,<6
                                                 <9,<10
                                      <7,<8



     Use the Venn Diagram to determine which 
     of the following statements are true?

       I.     <11 & <12 are adjacent.
       II.    <7 & <8 are vertical.
       III.   <9 & <10 are not adjacent.
       IV.    <5 & <6 are both congruent and adjacent.

       A.  I only
       B.  II only
       C.  III only
       D.  IV only
       E.  I and III only
       F.  I and IV only.
       G.  I, III, and IV.


Title: 9 (10 of 11)
                       Homework:
          p. 99 #1, 4, 8,10, 11

          p. 104 #1, 22, 36­40

          p. 112 #1, 3­9,12­17,19,22, 27

          Complete worksheet!



Title: 10 (11 of 11)

								
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