Download Lesson 1.5 - Conditional Statements

Geometry
Name: _______________________________
Unit 1: Lesson 1.5
Date: _________________ Period: _______
Conditional Statements
Essential Questions:
o
Why are some statements bi-conditional and other statements are not?
Goal:
 I will understand that a relationship exists between the hypothesis and conclusion of a conditional
statement.
Key Ideas/Vocabulary:

CONDITIONAL STATEMENT  a ________ statement that involves a comparison of _______ or
_________ (a.k.a IF-THEN STATEMENT)
A conditional statement has two parts: the hypothesis (p) and the conclusion (q).
“If p, then q.”

Symbol:
pq
CONVERSE  is formed by interchanging the hypothesis and conclusion in the conditional statement.
“If q, then p.”
Symbol: q  p
“A converse and conditional statement can be ________ or __________.”

COUNTEREXAMPLE  at least one fact or argument that indicates a mathematical theorem is NOT
true.

BI-CONDITIONAL  a conditional and its converse where the converse is also true. “if and only if”
Example: “A right angle is an angle that measures 900.”
Symbol:
pq
Section 1: Conditional Statements and Converses
1) Identify the hypothesis and conclusion of each YT 1) Identify the hypothesis and conclusion of
statement. Then write each statement in if-then
each statement. Then write each statement in ifform.
then form.
“Every student who takes geometry in Mr. Marttila’s class
“School begins only if it is 7:30 A.M.”
gets an A on the Geometry Test”
Answer:
Answer:
If-Then Statement:_________________________
2) Identify the hypothesis and conclusion of each
statement. Then write each statement in if-then
form.
“A five-sided polygon is a pentagon”
Answer:
If-Then Statement:_________________________
YT 2) Identify the hypothesis and conclusion of
each statement. Then write each statement in ifthen form.
“To find the distance between two points, you
can use the Distance Formula”
Answer:
If-Then Statement:________________________
If-Then Statement:_________________________
Section 2: Converse and Bi-conditionals
3) Write the converse and bi-conditional of the
statement.
“If the date is July 4th, then it is Independence Day.”
YT 3) Write the converse and bi-conditional of the
statement.
“If you visited the Statue of Liberty, then you’ve been to New York.”
Answer:
Answer:
Converse:_________________________________
Converse:_________________________________
Bi-Conditional:_____________________________
Bi-Conditional:_____________________________
Section 3: Truth Values of Conditional Statements and Converses
4) Decide whether the statement and its
YT 4) Decide whether the statement and its
converse are true.
converse are true.
If mA  30  , then A is acute.
If it lives in water, then it is a fish.
Answer:
Answer:
CONDITIONAL 
TRUE OR FALSE
CONVERSE 
TRUE OR FALSE
5) Decide whether the statement and its
converse are true.
If two lines intersect, then they are not parallel.
Answer:
CONDITIONAL 
TRUE OR FALSE
CONVERSE 
TRUE OR FALSE
Section 4: Writing a Counterexample
6) Write a counterexample to show that the
following conditional statement is false.
If 2 x 2  x  3  0 , then x  1.
Answer:
CONDITIONAL 
CONVERSE 
TRUE OR FALSE
TRUE OR FALSE
YT 5) Decide whether the statement and its
converse are true.
If you have vertical angles, then the angles are
congruent.
Answer:
CONDITIONAL 
TRUE OR FALSE
CONVERSE 
TRUE OR FALSE
YT 6) Write a counterexample to show that the
following converse of the conditional is false.
If the number is divisible by 3, then the number is
odd.
Answer:
7)
Section 5: Using Postulates
Use the diagram at the right to give
examples of Postulates 5 through 11.
Homework:
Conditional Statements – Supplement Worksheet # 7
Lesson Summary: Translate one of the Postulates 5, 6, 8, or 9 to “if-then” form
Name______________________________________________Period__________Date____________________
CONDITIONAL STATEMENTS - SUPPLEMENT WORKSHEET # 7
USE THE CONDITIONAL STATEMENT TO ANSWER QUESTIONS 1 – 3.
If you like the Phillies, then you like Baseball.
1.) Underline the hypothesis of this statement.
2.) Circle the conclusion of this statement.
3.) Write the converse of the statement:
____________________________________________________________________
USE THE CONDITIONAL STATEMENT TO ANSWER QUESTIONS 4– 6.
If you listen to One Direction, then you like pop rock.
4.) Identify the hypothesis:_____________________________________________
5.) Identify the conclusion:_____________________________________________
6.) Write the converse of the statement:
____________________________________________________________________
7.) Use the given information to write a conditional statement:
Hypothesis: You have perpendicular lines
Conclusion: you have 4 right angles
____________________________________________________________________
8.) Use the given information to write a conditional statement:
Hypothesis: You have two angles
Conclusion: the angles are supplementary
____________________________________________________________________
9.) Write a conditional statement regarding an isosceles triangle.
____________________________________________________________________
10.) Write a conditional statement regarding an obtuse triangle. Then the converse.
Conditional:___________________________________________________________
Converse:_____________________________________________________________
11.) Write a bi-conditional statement regarding a scalene triangle.
____________________________________________________________________
12.) Write a bi-conditional statement regarding a Disney character.
____________________________________________________________________
13.) Find a counterexample for the statement.
“If you play a musical instrument then you are in the school band.”
____________________________________________________________________
14.) Find a counterexample for the statement.
“If you don’t eat beef, then you are a vegetarian.”
____________________________________________________________________
15.) Find a counterexample for the statement.
If 6x – 3 > 1, then x > 2.
____________________________________________________________________
16.) Find a counterexample for the statement.
If today is Sunday, you go to school tomorrow.
____________________________________________________________________
17.) Find a counterexample for the converse of the conditional statement.
If u > -5, then u is a positive.
____________________________________________________________________