Geometry 2-1 Notes: Conditional Statements
Name _____________________________
Conditional Statement: _____________________________________________________________________
Has 2 parts: Hypothesis - ________________________ and Conclusion - _______________________
Example 1: Identifying the Hypothesis and Conclusion
Underline the hypothesis and circle the conclusion of each conditional statement.
a. If two lines are parallel, then the lines are coplanar.
b. The month is September if today is the first day of fall.
c. If y – 3 = 5, then y = 8.
d. You are in the state of Illinois when you are in the city of Chicago.
Example 2: Finding a Counterexample
Find a counterexample to show that each conditional statement is false.
a. If it is the weekend, then it is Saturday.
b. If a number is even, then it is divisible by 4.
c. If x2 ≥ 0, then x ≥ 0.
Converse: ________________________________________________________________________________
Example 3: Writing the Converse of a Conditional Statement
Write the converse of each conditional statement.
a. If two lines are not parallel and do not intersect, then they are skew.
Converse: __________________________________________________________________________
__________________________________________________________________________________
b. If two lines intersect to form right angles, then they are perpendicular.
Converse: __________________________________________________________________________
__________________________________________________________________________________
Example 4: Determining if the Converse is true
Write the converse of each given conditional statement. Determine if the converse is also a true statement.
a. If a figure is square, then it has four sides.
Converse: _______________________________________________________________________
Truth value: _____________________ Counterexample: __________________________________
b. If a = 5, then a2 = 25.
Converse: _______________________________________________________________________
Truth value: _____________________ Counterexample: __________________________________
Geometry 2-2 Notes: Biconditionals and Definitions
Biconditional Statement: If a __________________ and its __________________ are both true, you can write
one statement by joining the two with ____________________________________________.
Example 1: Writing a Biconditional Statement
Each conditional statement is true. Consider each converse. If the converse is true, combine the statements
and write them as a biconditional. If not, write not reversible.
a. If two angles have the same measure, then the angles are congruent.
Converse: __________________________________________________________________________
__________________________________________________________________________________
Biconditional: ______________________________________________________________________
__________________________________________________________________________________
b. If three points are collinear, then they lie on the same line.
Converse: __________________________________________________________________________
__________________________________________________________________________________
Biconditional: ______________________________________________________________________
__________________________________________________________________________________
c. If a figure is a square, then it has four right angles.
Converse: __________________________________________________________________________
__________________________________________________________________________________
Biconditional: ______________________________________________________________________
Example 2: Separating a Biconditional into Parts
Write the two conditional statements that make up each biconditional.
a. A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
1. ________________________________________________________________________________
2. ________________________________________________________________________________
b. A number is prime if and only if it has only two distinct factors, 1 and itself.
1. ________________________________________________________________________________
2. ________________________________________________________________________________
Example 3: Good Definitions
A good definition must be __________________, ____________________, and _______________________.
Explain why each of the following is not a good definition.
a. An angle that is not acute is obtuse. _____________________________________________________
b. Lines that do not intersect are parallel. ___________________________________________________
Sec 2-1 & 2-2 HW: ________________________________________________________________________