Geometry; 9/27

We answered some homework questions together and then spent some time working through a few major topics that will show up on the quiz tomorrow.  How to work with conditional statements (and the key words and phrases), how to write algebra proofs, and how to write geometric proofs were all skills that were reviewed.  The students then got started on the task of going through the chapter quiz review sheet.   Chapter 2 quiz is tomorrow.


Assignment:  Chapter 2 Quiz review


Review Sheet answers

Using Deductive Reasoning

1.  hypothesis:  line AB intersects line CD at X
     conclusion:  A, X, and C are coplanar
2.  Hypothesis:  I finish my homework
     conclusion:  I can ride my bicycle
3.  initial statement:  false
     Converse:  If M is midpoint of segment AB, then AM = MB;  converse is true
4.  transitive prop. =
5.  reflexive prop. =
6.  substitution prop. =
7.  symmetric prop. =
8.  addition prop. =
9.  angle bisector theorem
10.  segment addition postulate
11.  angle addition postulate
12.  midpoint theorem
13.  definition of angle bisector

Algebra proof #5                                                          

-3(x + 2) = 16 - x            given                                    
-3x - 6 = 16 - x               distributive prop                  
-6 = 16 + 2x                    addition prop. =                  
-22 = 2x                          subtraction prop. =              
-11 = x                            division prop. =                  

 Algebra proof  #7

6(x - 6) = x(16 - 7)     given
6x - 36 = 16x - 7x      distributive prop.
6x - 36 = 9x                combine like terms
-36 = 3x                       subtraction prop. =
-12 = x                         division prop. =


Properties of Algebra

1.  addition prop. =
2.  division prop. =
3.  multiplication prop. =
4.  subtraction prop. =
5.  division prop. =
6.  distributive prop.
7.  transitive prop. =
8.  symmetric prop. =
9.  addition prop. =
10.  transitive prop. =
11.  subtraction prop. =
12.  skip
13.  skip
14.   proof
           1.  given
           2.  reflexive
           3.  addition prop. =
           4.  segment addition postulate
           5.  transitive / substitution

Proving Theorems

1.  def. of midpoint
2.  def. of angle bisector
3.  midpoint theorem
4.  angle bisector theorem
5.  midpoint theorem
6.  segment addition postulate
7.  angle addition postulate
8.  angle addition postulate
9.  def. of segment bisector
10.  55
11.  65
12.  80
13.  9
14.  8
15.  4.5
16.  3.5
17.  items in a proof
        1.  given                2.  word definitions      
        3.  postulates         4.  theorems

Practice Proofs

1.  given
2.  def. of midpoint
3.  definition of congruence
4.  segment addition postulate
5.  substitution
6.  combine like terms / simplify
7.  division prop. =
8.  substitution prop. =


1.  given
2.  angle addition postulate
3.  substitution prop. =
4.  angle addition postulate
5.  transitive prop. / substitution prop.