Geometry Notes
Name ______________________________
2.1 Conditional Statements
Date ________________ Period ______
Objective
Recognize and analyze a conditional statement.
Write postulates about points, lines, and planes using conditional statements
Conditional Statements
Example 1
Underline the hypothesis. Circle the conclusion.
a.
If today is Thanksgiving Day, then today is Thursday.
b. A number is a rational number if it is an integer.
Example 2
Write a conditional statement from the following.
a. An obtuse triangle has exactly one obtuse angle.
b.
c. Two angles that are complementary are acute.
Conditional Statement
Words
Symbols
A statement that can be written in the form “if h, then c.”
Hypothesis
The part h of a conditional statement following the word
“if.”
Picture of Venn Diagram
Conclusion
The part c of a conditional statement following the word
“then.”
Converse
The statement formed by exchanging the hypothesis
and conclusion.
Words
Symbols
Inverse
The statement formed by negating the hypothesis
and conclusion.
Contrapositive
The statement formed by both exchanging and
negating the hypothesis and conclusion.
Example 3
Write the converse, inverse, and contrapositive of the conditional statement.
Then find the truth value of each.
Conditional: If Maria's birthday is February 29th, then she was born in a leap year.
Converse: __________________________________________________________________________________________
___________________________________________________________________________________________
Inverse: ___________________________________________________________________________________________
___________________________________________________________________________________________
Contrapositive: _____________________________________________________________________________________
___________________________________________________________________________________________
Example 4
Determine if the conditional is true. If false, give a counterexample.
a. If this month is August, then next month is September.
b. If two angles are acute, then they are congruent.
Example 5
Decide whether or not the following statement is true or false. If false, provide a counterexample.
a. If a number is odd, then it is divisible by 3.
b. If 𝑛2 = 144, then n = 12.