QuestionDetermine if the statements are the inverse, converse, or contrapositive of: "If two lines form equal adjacent angles, then they are perpendicular." a. If two lines are not perpendicular, then they do not form equal adjacent angles. b. If two lines do not form equal adjacent angles, then they are not perpendicular.
Studdy Solution
STEP 1
Assumptions1. The original statement is "If two lines form equal adjacent angles, then the lines are perpendicular." . We have to determine whether the given statements are the inverse, converse, or contrapositive of the original statement.
STEP 2
Let's define what inverse, converse, and contrapositive mean in the context of conditional statements.
1. Inverse The inverse of a statement "If, then Q" is "If not, then not Q."
2. Converse The converse of a statement "If, then Q" is "If Q, then."
. Contrapositive The contrapositive of a statement "If, then Q" is "If not Q, then not."
STEP 3
Let's identify the hypothesis () and the conclusion (Q) in the original statement.
The original statement is "If two lines form equal adjacent angles (), then the lines are perpendicular (Q)."
STEP 4
Now, let's analyze statement a "If two lines are not perpendicular, then they do not form equal adjacent angles."
In this statement, "two lines are not perpendicular" is not Q and "they do not form equal adjacent angles" is not. So, this statement is the contrapositive of the original statement.
STEP 5
Next, let's analyze statement b "If two lines do not form equal adjacent angles then they are not perpendicular."
In this statement, "two lines do not form equal adjacent angles" is not and "they are not perpendicular" is not Q. So, this statement is the inverse of the original statement.
So, statement a is the contrapositive of the original statement and statement b is the inverse of the original statement.
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