Geometry
Date_____________




Name___KEY__________________
Today, we will
define and identify converse, inverse, contrapositive and bi-conditional statements
understand deductive reasoning and the Laws of Logic
and by the end of class, you will
write converse, inverse, contrapositive and bi-conditional statements
apply the laws of logic to real world situations
Analyzing Conditional Statements
A ___Conditional Statement____ is a logical argument that has two parts, a hypothesis and a
conclusion.
If the weather is rainy , then there are clouds in the sky.
hypothesis
conclusion
Example 1
Rewrite the conditional statement in if-then form.
a. All birds have feathers.
If an animal is a bird, then it has feathers.
b. Two angles are supplementary if they are a linear pair.
If two angles are a linear pair, then they are supplementary.
The _negation________ of a statement is the opposite of the original statement.
Statement 1 The ball is red.
Statement 2 The cat is not black.
Negation 1
Negation 2
The ball is not red.
The cat is black.
Converse – Flip (Switch) the hypothesis and conclusion of a conditional statement.
Inverse – Negate both the hypothesis and conclusion of a conditional statement.
Contrapositive – Flip (Switch) and negate the hypothesis and conclusion of a conditional statement.
Biconditional statement – Put “if and only if” between the hypothesis and the conclusion of a
conditional statement.
Example 2
Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement
“Guitar players are musicians.”
Conditional –
If a person is a guitar player, then they are a musician.
Converse –
If a person is a musician, then they are a guitar player.
Inverse –
If a person is not a guitar player, then they are not a musician.
Contrapositive –
If a person is not a musician, then they are not a guitar player.
Example 3
Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement
“Harry Potter fans are awesome.”
Conditional – If you are a Harry Potter fan, then you are awesome.
Converse – If you are awesome, then you are a Harry Potter fan.
Inverse – If you are not a Harry Potter fan, then you are not awesome.
Contrapositive – If you are not awesome, then you are not a Harry Potter fan.
**Every definition can be written as a conditional statement in if-then form or as its converse. Both
statements will be true.**
Perpendicular Lines
Definition – If two lines intersect to form a right angle, then
they are perpendicular.
m
Converse – If two lines are perpendicular, then they intersect
To form a right angle.
Example 4
Write the definition of perpendicular lines as a biconditional.
n
m n
Two lines intersect to form a right angle if and only if they are perpendicular.
Example 5
Rewrite the statements as a biconditional.
If Mary is in theater class, then she is in the fall play. If Mary is in the fall play, then she is in theater
class.
Mary is in theater class if and only if she is in the fall play.
Applying Deductive Reasoning
_Deductive Reasoning_______ uses facts, definitions, accepted properties, and the laws of logic to
form a logical argument.
Laws of Logic:
Law of Detachment – If the hypothesis of a true conditional statement is true, then the
conclusion is also true.
Every Monday, Susie eats a banana for breakfast. Today is Monday.
Therefore, Susie had a banana for breakfast.
Law of Syllogism – If the statement if p then q is true and the statement if q then r is true, then the
statement if p then r is true.
If Bob has Mrs. Schutte for Geometry, then he’ll work and study hard.
If Bob works and studies hard, then he’ll get an A for the year.
Therefore, if Bob has Mrs. Schutte for Geometry, he’ll get an A for the year.
If p, then q.
 If p, then r.
If q, then r. 
Example 1
Use the Law of Detachment to make a valid conclusion in the true situation.
a. If two segments have the same length, then they are congruent. You know that BC = XY.
BC  XY
b. Every Friday and Saturday night, Becky rents a Redbox DVD. Today is Friday.
If it is a Friday or Saturday night, then Becky rents a Redbox DVD.
Today is Friday.
Therefore, Becky will rent a Redbox DVD.
Example 2
If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of
true statements.
a. If Jeff takes Chemistry this year, then he’ll take it 8th period.
If Jeff has it 8th period, then Adam is Jeff’s lab partner.
If Jeff takes Chemistry this year, then Adam is Jeff’s lab partner.
b. If x2 > 25, then x2 > 20.
If x > 5, then x2 > 25.
If x > 5, then x2 > 25.
If x2 > 25, then x2 > 20.
If x > 5, then x2 > 20.
c. If a polygon is regular, then all angles in the interior of the polygon are congruent.
If a polygon is regular, then all of its sides are congruent.
No conclusion