# 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.

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

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
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
Hopefully, these are all review…
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
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
z = -1                 Division property
PROBLEM OF THE DAY

Before you leave…

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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