1. Conditional Statements
Unit 3: Proofs
Conditional
Statements
Lesson 2-1 Conditional Statements

2. Conditional Statement
Definition:
A conditional statement is a statement that can be written in if-then form.
“If _____________, then ______________.”
Example:
If your feet smell, then it is time to get new shoes.
Continued……
Lesson 2-1 Conditional Statements

3. Conditional Statement - continued
Conditional Statements have two parts:
The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.)
The hypothesis is the given information, or the condition.
The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.)
The conclusion is the result of the given information.
Lesson 2-1 Conditional Statements

4. Lesson 2-1 Conditional Statements
Writing Conditional Statements
Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion.
Hint: Turn the subject into the hypothesis.
Example 1:
Vertical angles are congruent.
can be written as...
Conditional Statement:
If two angles are vertical, then they are congruent.
Example 2:
Good students love math
can be written as...
Conditional Statement:
If a student is good then he/she loves math
Lesson 2-1 Conditional Statements

5. Two angles are vertical implies they are congruent.
If …Then vs. Implies
Another way of writing an if-then statement is using the word implies.
If two angles are vertical, then they are congruent.
Two angles are vertical implies they are congruent.
Lesson 2-1 Conditional Statements

6. Conditional Statements can be true or false:
A conditional statement is false only when the hypothesis is true, but the conclusion is false.
A counterexample is an example used to show that a statement is not always true and therefore false.
Statement:
If you live East Cobb then you go to Pope.
Yes !!!
Is there a counterexample?
Counterexample:
I live in East Cobb but I go to Walton. 
Therefore () the statement is false.
Lesson 2-1 Conditional Statements

7. Lesson 2-1 Conditional Statements
Symbolic Logic
Symbols can be used to modify or connect statements.
Symbols for Hypothesis and Conclusion:
Hypothesis is represented by “p”.
Conclusion is represented by “q”.
if p, then q or
p implies q
Continued…..
Lesson 2-1 Conditional Statements

8. Symbolic Logic - continued
if p, then q
or p implies q
p  q
is used to represent
Example:
p: a number is prime
q: a number has exactly two divisors
pq:
If a number is prime, then it has exactly two divisors.
Continued…..
Lesson 2-1 Conditional Statements

9. is used to represent the word
Symbolic Logic - continued ~
is used to represent the word
“not”
Example 1:
p: the angle is obtuse
~p:
The angle is not obtuse
Note:
~p means that the angle could be acute, right, or straight.
Example 2:
p: I am not happy
~p:
I am happy
~p took the “not” out- it would have been a double negative (not not)
Lesson 2-1 Conditional Statements

10. Forms of Conditional Statements
Converse: Switch the hypothesis and conclusion (q  p)
pq If two angles are vertical, then they are congruent.
qp If two angles are congruent, then they are vertical.
Continued…..
Lesson 2-1 Conditional Statements

11. Forms of Conditional Statements
Inverse: State the opposite of both the hypothesis and conclusion. (~p~q)
pq : If two angles are vertical, then they are congruent.
~p~q: If two angles are not vertical, then they are not congruent. (is this true?)
Lesson 2-1 Conditional Statements

12. Forms of Conditional Statements
Contrapositive: Switch the hypothesis and conclusion and state their opposites. (~q~p)
pq : If two angles are vertical, then they are congruent.
~q~p: If two angles are not congruent, then they are not vertical.
Lesson 2-1 Conditional Statements

13. Forms of Conditional Statements
Contrapositives are logically equivalent to the original conditional statement.
If pq is true, then qp is true.
If pq is false, then qp is false.
Lesson 2-1 Conditional Statements

14. Lesson 2-1 Conditional Statements
Biconditional
When a conditional statement and its converse are both true, the two statements may be combined.
Use the phrase if and only if (sometimes abbreviated: iff)
Statement: If an angle is right then it has a measure of 90.
Converse: If an angle measures 90, then it is a right angle.
Biconditional: An angle is right if and only if it measures 90.
Lesson 2-1 Conditional Statements

15. Lesson 2-1 Conditional Statements
Why do we care?
We are going to start doing proofs. Essentially we need a reason for what we are concluding.
Lesson 2-1 Conditional Statements

16. Lesson 2-1 Conditional Statements
What can you conclude?
If Emma gets an A on her Geometry test, then her Mom will let her go to a concert.
A) Emma got a 96 on her Geometry test.
B) Emma went to a concert.
C) Emma did not go to a concert.
Lesson 2-1 Conditional Statements

17. Lesson 2-1 Conditional Statements
What can you conclude?
If Jake passes his driving test he will drive to school
Jake failed his driving test.
Jake is not driving to school?
Lesson 2-1 Conditional Statements

18. Lesson 2-1 Conditional Statements
What can you conclude?
Anna will wear white on Friday if and only if there is a “white out” football game.
The football game was cancelled.
Lesson 2-1 Conditional Statements

19. Lesson 2-1 Conditional Statements
What can you conclude?
Corresponding angles are congruent if and only if two parallel lines are cut by a transversal.
Angles one and two are corresponding and congruent.
Lesson 2-1 Conditional Statements

20. Lesson 2-1 Conditional Statements
What can you conclude?
The jury will find him guilty if and only if all twelve jurors vote guilty.
Mr. Sever was found not guilty.
Lesson 2-1 Conditional Statements