Geometry Notes – 2.1, 2.2, and 5.4 – Statements and Reasoning
Name: _____________________
2.1.1: CONDITIONAL STATEMENTS (Pg 80)
A _______________________ is an if-then statement that contains two parts
The part following the if is the ____________________.
The part following the then is the ____________________.
Ex1: Identify the hypothesis and conclusion.
If you live in Fort Collins, then you live in Colorado.
Ex2: Identify the hypothesis and conclusion.
If two lines are parallel, then the lines are coplanar.
Hypothesis:
Hypothesis:
Conclusion:
Conclusion:
The ______________________ of a statement tells whether it is “true” or “false”.
Ex3: Write the statement as a conditional.
An acute angle measures less than 90 degrees.
Conditional Statement:
Ex4: Write a counterexample to prove the
conditional false
If x 2  0 , then x  0
(The counterexample for the conditional is when the ___________________ is true but the ________________
is false.)
2.1.2: CONVERSES (Pg 81)
The ______________________ of a conditional switches the hypothesis and the conclusion.
Ex5: Write the converse of the conditional and determine the truth value of each.
Conditional: If two lines are not parallel and do not intersect, then they are skew.
T or F
Converse:
T or F
Ex6: Write the converse of the conditional and
determine the truth value of each
Conditional: if x = 9, then x + 3 = 12
T or F
Ex7: Write the converse of the conditional and
determine the truth value of each
Conditional: If a = 5, then a 2  25
T or F
Converse:
Converse:
T or F
T or F
2.2.1: BICONDITIONALS (Pg 87)
When a conditional and its converse are true, you can combine them as a true ___________________________.
You can combine them by using the phrase _______________________.
Ex8: Write the converse of the conditional. If both are true, combine the statements as a biconditional
Conditional: If two angles have the same measure, then they are congruent
Converse:
Biconditional:
Ex9: Write the two statements that form the biconditionals.
Biconditional: You live in the capitol of the United States if and only if you live in Washington, D.C.
Conditional:
Converse:
5.4.1: NEGATIONS, INVERSES, AND CONTRAPOSITIVES (Pg 280)
The negation of a statement has the ____________________ __________________ of the original statement.
Ex10: Find the negation of the following statement.
Original Statement: Two angles are congruent
Negation:
The inverse of a conditional statement negates both the _________________ and the ____________________.
Ex11: Find the inverse of the following conditional.
Conditional: If a figure is a square, then it is a rectangle.
Inverse:
The contrapositive of a conditional statement __________________ the hypothesis and conclusion and
_________________ both.
Ex12: Find the contrapositive of the following conditional.
Conditional: If a figure is a rectangle, then it is a quadrilateral
Contrapositive:
Ex13: Write the inverse and contrapositive of Maya Angelou’s statement.
Statement: “If you don’t stand for something, then you’ll fall for anything.”
Inverse:
Contrapositive:
5.4.2: IDENTIFYING CONTRADICTIONS (Pg 282)
Ex14: Identify the two statements that contradict each other.
I. FG is parallel to KL
II. FG  KL
III. FG is perpendicular to KL
I and II: Can two segments be parallel and congruent? ___________
II and III: Can two segments be congruent and perpendicular? ______________
I and III: Can two segments be parallel and perpendicular? _________