2 2Biconditional Algebraic4b by 65AKdK

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									 Sec. 2.2 Biconditional Statements
Sec 2.5 Using Algebraic Properties
   1. Please take a seat in any open seat.

   2. Make sure to pick up your POD sheet, your
      folder, and a calculator if you need one.

   3. Please grab a Sudoko puzzle sheet.

   3. Grab a pencil and sharpen it if needed.

   4. Please be ready to start working when the bell
      rings.
   **If you were absent last class, please talk to your
      partner about what we covered in class last
      time. You can also consult the lesson plans (on
      the left wall) to see what you missed.
    Chapter 1 Test
Class Average: 84.90

Range: 15

Grade Breakdown:
  A - 10
  B-2
  C-2
  D-0
  F–0

So, what percentage of the class failed?
QUICK QUESTION
How would you define
perpendicular lines?

Perpendicular lines are
those which intersect if
they form a right angle


     Now, write this definition as an if-then
           conditional statement…
                    If two lines are
                   perpendicular, then
                  they intersect to form
                       a right angle.

       Now, write the converse of this
          conditional statement…

If two lines intersect to form a right
  angle, then they are perpendicular.
QUICK QUESTION
How would you go about
combining the conditional
statement and the converse?
If two lines are perpendicular, then they intersect to
                   form a right angle.

If two lines intersect to form a right angle, then they are
                         perpendicular.


                 if and only if…
BICONDITIONAL
STATEMENTS
 A biconditional statement is one that
  contains the phrase “if and only if.”
 Writing a biconditional statement is
  equivalent to writing a conditional
  statement and its converse.

   Two lines are perpendicular
         IF AND ONLY IF
the lines intersect to form a right
                angle.
Example 3: Analyzing
Biconditional Statements
  Consider the following statement:
      x = 3 if and only if x2 = 9.
  Is this a biconditional statement?
The statement is biconditional because it
    contains the phrase “if and only if.”
         Is the statement true?
        Conditional statement:
           If x = 3, then x2 = 9.
   Converse: If x2 = 9, then x = 3.
 The first part of the statement is true, but
        what about -3? That makes the
      second part of the statement false.
CELL PHONE
  BREAK

 What is the object most choked on by
              Americans?

              Toothpick
Algebraic Properties
    Please turn to Pg. 96
    Hopefully, these are all review…
    Addition property
    Subtraction property
    Multiplication property
    Division property
    Reflexive property
    Symmetric property
    Transitive property
    Substitution property
   Distributive Property
a (b + c) = ab + ac

Each of these properties can be
used to solve equations and other
problems.
Example:
 x+3=7
By subtracting 3 from each side of
the equation, you obtain 4.
WHICH PROPERTY DID WE USE?
 Example 1: Writing Reasons


Solve 5x – 18 = 3x +2
  5x – 18 = 3x + 2           Given
     2x – 18 = 2      Subtraction property
       2x = 20         Addition property
        x = 10         Division property
 Example 2: Writing Reasons

Solve: 55z – 3(9z + 12)= -64
55z – 3(9z + 12)= -64        Given
55z – 27z – 36 = -64 Distributive property
28z – 36 = -64              Simplify
28z = -28              Addition property
z = -1                 Division property
PROBLEM OF THE DAY

Before you leave…
 On your POD sheets please complete
 the following on your OWN.

Guided Practice (2.2 pp. 82)
#3, 8

Practice and Applications
(2.4 pp. 99)
#15
Assignment

• Finish Workbook Section
  2.2 and Section 2.4

								
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