Chapter 2.1 – If-Then Statements
and Postulates
Chapter 2.2 – Definitions and
Biconditional Statements
Objective: Be able to write if-then
statements, the converse, inverse,
and contrapositive.
Obj: Be able to recognize and use
definitions.
Before You Begin…
• Read sections 2.1 and 2.2 in your book.
Vocabulary
•Conditional Statement: an if-then sentence
with a hypothesis and a conclusion
•Hypothesis: the “if part” of a conditional
statement
•Conclusion: the “then part” of a conditional
statement
•Converse: Formed by switching the
hypothesis and conclusion of a
conditional statement
More Vocabulary
•Negation: the negative of a statement
•Inverse: Formed when you negate the
hypothesis and conclusion of a
conditional statement
•Contrapositive: Formed when you negate
the hypothesis and
conclusion of the converse
of a conditional statement
Postulates
•Postulate 5: Through any two points there exists exactly
one line
•Postulate 6: A line contains at least two points
•Postulate 7: If two lines intersect, then their
intersection is exactly one point
•Postulate 8: Through any three non-collinear points
there exists exactly one plane
•Postulate 9: A plane contains at least three noncollinear points
•Postulate 10: If two points lie in a plane, then the line
containing them lies in the plane
•Postulate 11: If two planes intersect, then their
intersection is a line
A little more Vocabulary
•Bi-conditional Statement:
a statement that contains the
phrase “if and only if”
Example
Identify the hypothesis and conclusion
If the weather is warm, then we should go swimming.
Example
Rewrite the conditional statement in if-then form
An acute angle is an angle that measures less than 90 degrees
Example
Decide whether the statement is true or false.
If false, provide a counterexample.
Example
If x is odd, then 2x is even.
Example
Example
Example
Example
HOMEWORK
Section 2.1 and 2.2
homework assignment