Transcript Conditional Statements

CONDITIONAL
STATEMENTS
Section 2-1
Objectives

To recognize conditional statements.

To write converses of conditional statements.
Have you ever heard a person say: If you are not
completely satisfied, then your money will be refunded?
This is an if-then statement called a ______________.
Every conditional statement has two parts.
The part following the if is the _____________.
The part following the then is the ___________.
Example 1:
Identify the Hypothesis
and the Conclusion
If today is the first day of fall, then the month is
September.
Hypothesis:
Conclusion:
Example 2:
Identify the Hypothesis
and the Conclusion
If you want to be fit, then get plenty of exercise.
Hypothesis:
Conclusion:
Converse
To find the Converse of a Conditional
-Switch the Hypothesis and Conclusions around,
But you keep the “IF” and “Then” where they are.
Write the converse of the conditional
statement.
Example :
If two lines are not parallel and do not intersect,
then they are skew lines.
Write the converse of the conditional
statement
Example :
If you eat your vegetables, then you grow.
Write the converse of the conditional
statement
Example:
If a triangle is a right triangle, then it has a 90
degree angle.
Truth Values (true or false?)
Converses are NOT ALWAYS TRUE.
Write the converse of the conditional AND
determine it’s truth value.
If a figure is a square, then it has four sides.
Truth Values (true or false?)
Example: Write the converse of the conditional
AND determine it’s truth value.
If two lines do not intersect, then they are parallel.
Truth Values (true or false?)
Example: Write the converse of the
conditional AND determine it’s
truth value.
If x = 2, then |x| = 2.
BICONDITIONALS AND
DEFINITIONS
Section 2-2
Objectives

To write biconditionals.

To recognize good definitions.
Objective
A ______________ is the combination of a
conditional statement and its converse.
A biconditional (statement) contains the words
“___________________.”
Consider the true conditional statement. Write its
converse. If the converse is also true, combine the
statements as a biconditional.
1. Conditional: If two angles have the same
measure, then the angles are congruent.
Consider the true conditional statement. Write its
converse. If the converse is also true, combine the
statements as a biconditional.
2. Conditional: If three points are collinear, then they
lie on the same line.
Recognizing a Good Definition -
Use the examples to identify the
figures above that are polyglobs.
Write a definition of a polyglob by describing what a polyglob
is.
See Page 76
Show that the definition is reversible.
Then write it as a true biconditional.
1. Definition: Perpendicular lines are two lines that
intersect to form right angles.
Show that the definition is reversible.
Then write it as a true biconditional.
2. Definition: A right angle is an angle whose
measure is 90 (degrees).
Is the given statement a good definition?
Explain.
1.
An airplane is a vehicle that flies.
2.
A triangle has sharp corners.
3.
A square is a figure with four right angles.
DEDUCTIVE REASONING
“LAWS OF
DETACHMENT/SYLLOGISM”
Section 2-3
Classwork
Page 71
12 – 26 even, 54 – 58
Page 78
1 – 12, 27 – 35, 41 – 43
Page 84
1 – 15 odd
Page 102
44 - 51