Mrs. Scott
Modern Geometry
Name:_________________________
Date:__________________________
2.1 – Conditional Statements
Objectives for these sections:
1. Recognize the hypothesis and conclusion of a conditional statement.
2. Write a conditional statement and find a counterexample.
3. Write the converse of a conditional statement.
I. Conditional Statements (If-Then Statements)
“If you are not completely satisfied, then your money will be refunded.”
This is an example of a __________________________ statement.
Another name for an if-then statement is ____________________________.
Every conditional statement has ________ parts.
1) Following the if is the _________________________________.
2) Following the then is the _______________________________.
II. Example 1 – Identify the hypothesis and conclusion for each statement.
a) If Texas won the 2006 Rose Bowl football game, then Texas was college football’s 2005 national champion.
Hypothesis:
Conclusion:
b) If T – 38 = 3, then T = 41.
Hypothesis:
Conclusion:
c) If two lines are parallel, then the lines are coplanar.
Hypothesis:
Conclusion:
III. Example 2 - Write each sentence as a conditional
a) A rectangle has 4 right angles.
b) A tiger is an animal.
c) An integer that ends with 0 is divisible by 5.
d) A square has 4 congruent sides.
IV. Other Ways of Writing Conditionals
Example: Hypothesis (p) = It is snowing. Conclusion (q) = It is cold outside.
1. If p, then q.
2. P implies q.
3. P only if q.
4. Q if p.
V. Example 3 - Finding a Counter Example.
Show that these conditionals are false by finding a counterexample.
If it is February, then there are only 28 days in the month.
If x2 ≥ 0, then x ≥ 0.
Example 4 – Using a Venn Diagram
Draw a Venn diagram to illustrate this conditional: If you live in Chicago, then you live in Illinois.
Draw a Venn diagram to illustrate this conditional: If something is a cocker spaniel, then it is a dog.
VI. Writing the Converse of a Conditional
The _____________ of a conditional switches the ________________ and the _______________________.
Example 5 – Write the converse of the following conditional.
Conditional: If two lines intersect to form right angles, then they are perpendicular.
Hypothesis =
Conclusion =
Converse =
Conditional: If two lines are not parallel and do not intersect, then they are skew.
Hypothesis =
Conclusion =
Converse =
VII.
Determining the Truth of a Converse
Conditional statements can be ______________ or ______________.
Example – “If a number is divisible by 3, then it is also divisible by 9.”
1. Is the conditional true?
2. Is the converse of this statement always true?
Example 7 - Real World Connection
2.2 – Biconditionals and Definitions
Objectives for this section:
1. Write and separate a biconditional statement into parts.
2. Write a definition as a biconditional.
3. Recognize the difference between a good definition and not a good definition.
I.
Biconditional Statements
When a ________________________ and its ________________________ are both
________, you can combine them as a ___________________________.
 Combine into a single statement using “if and only if”
 Definitions can always be written as biconditional statements
Example - If 1 2, then m 1=m 2.
1. Is this conditional statement true?
2. Write the converse. Is the converse always true?
3. Write the biconditional statement.
II.
Writing a Biconditional
Example 1 – Consider this true conditional statement. Write its converse. If the converse is
also true, combine the statements as a biconditional.
Conditional: If two angles have the same measure, then the angles are congruent.
Converse:
The converse is also ________________.
Since both the conditional and its converse are true, combine them into a ___________________ –
using the phrase “___________________________”
Biconditional:
III.
Separating a Biconditional into Parts
Example 2 – Write two statements that form this biconditional about whole numbers:
A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
What is the Conditional Statement?
Conditional:
What is the Converse Statement?
Converse:
IV.
Biconditional Statements
I.
What is a Good Definition?
A good definition is a statement that can __________ you identify or classify an object.
A good definition uses ______________________________. The terms should be
commonly understood or already defined.
A good definition is precise. _____________ words such as large, sort of, and almost.
A good definition is ________________________. That means that you can write a good
definition as a __________________________________.
II.
Writing a Definition as a Bicondtional
Example 3 – Show that this definition of perpendicular lines is reversible. Then write it
as a true biconditional.
Definition: Perpendicular lines are two lines that intersect to form right angles.
Conditional:
Converse:
Biconditional:
III.
Good Definition?
A square is a figure with four right angles.
It is not a good definition. Why?
Mrs. Scott
Modern Geometry
Name:_____________________________
Date:______________________________
Determining Truth of Converses
Determine if the converses of these conditional statements are always true.
If not, give a counterexample. If they are true, write the biconditional statement.
1. If segments are congruent, then their lengths are equal.
Converse:
Converse True?:
2. If m1=120, then 1 is obtuse.
Converse:
Converse True?:
3. If Ed lives in Texas, then he lives south of Canada.
Converse:
Converse True?:
4. If 4x = 20, then x = 5.
Converse:
Converse True?:
5. If B is between A and C, then AB+BC=AC.
Converse:
Converse True?: