Geometry
Notes
Name_______________________________
Date_______________ Pd______________
Warm up
1. If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true
statements.
If the sun is out today, then Matt will go to the pool.
If Matt goes to the pool, then he will go swimming.
2. Use the Law of Detachment to make a valid conclusion given the following statements.
In the winter, the sun rises after 7 am. It is December.
3. Use the given conditional statement to find the following:
“If you are out of milk, then you will go to the store.”
Converse –
Inverse –
Contrapositive –
4.
A biconditional statement must contain the phrase _______________
5.
Find a counter example to disprove the conjecture:
All 3 sided figures have at least one 90 degree angle.
6. Sketch the next figure in the sequence.
Recall Conditional Statements
Conditional Statements
Ex: Identify the Hypothesis and the Conclusion: “Peggy will wear her helmet, if she is riding her
bike”
Hypothesis:
Conclusion:
Write the converse, inverse and contrapositive:
Converse:
Inverse:
Contrapositive:
Recall Negation: The opposite of a statement.
“NOT”
Ex: Negate the following: I am a girl.
SYMBOLIC NOTATION:
Conditional
p  q
Converse
q  p
Inverse
~p  ~q
Contrapositive
~q  ~p
Biconditional
p q
(  ) means “implies”
(~) means negation – “not p” is written ~p
() means “therefore”
Example 3:
Let p be “the car is running” and let q be “the key is in the ignition”
a. Write the conditional statement p  q in words.
b. Write the converse in words and symbolic notation _____________
c. Write the inverse in words and symbolic notation _____________
d. Write the contrapositive in words and symbolic notation _____________
Geometry
Notes
Name_______________________________
Date_______________ Pd______________
More about Biconditional
Remember: Always has the words IF AND ONLY IF in the middle of the sentence.
A biconditional can be broken into a conditional statement and its converse.
Both must be true.
Example 4: An angle is a right angle if and only if it measures 90 degrees.
1) Conditional
2) Converse
Examples 5 & 6: Write the converse of the statement. If the conditional statement
and the converse are true then write the biconditional statement.
Example 5: If you have a perfect season then you won all your games.
Converse:
Biconditional:
Example 6: If the road is wet, then it is raining.
Converse:
Biconditional:
(MORE ON BACK)
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Truth Tables
truth value –
truth table –
Conditional
hypothesis conclusion
p
q
Conditional
Statement
Consider: If you get an A, then I will give you $5.
pq
Note: Contrapositive has the same truth value as the conditional statement.
Inverse has the same truth value as converse.