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Lesson 2-3
Conditional
Statements
Lesson 2-1 Conditional
Statements
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Conditional Statement
Definition: A conditional statement is a statement that
can be written in if-then form.
“If _____________, then ______________.”
Example:
If we practice hard, then we will win
tomorrow.
Continued……
Lesson 2-1 Conditional
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Conditional Statements have 2 parts:
•The hypothesis follows the word “if”. It is the
given information or the condition.
•The conclusion follows the word “then”. It is
the result of the given information.
Example 1:
If a polygon has six sides,
Hypothesis
then it is a hexagon.
Conclusion
Lesson 2-1 Conditional
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Writing Conditional Statements
When writing conditional statements, turn the
subject into the hypothesis and the predicate into
the conclusion.
Example 1: Vertical angles are congruent.
Conditional If two angles are vertical, then they are congruent.
Statement:
Example 2: Adjacent angles have a common side.
Conditional If two angles are adjacent, then they have a
Statement: common side.
Lesson 2-1 Conditional
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If …Then vs. Implies
Another way of writing an if-then statement is using
the word implies.
If two angles are vertical, then they are congruent.
Two angles are vertical implies they are congruent.
Lesson 2-1 Conditional
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Logic Symbols





p: hypothesis
q: conclusion
pq: If “hypothesis”, then “conclusion”.
~: “not”
 : “and” (conjunction)
: “or” (disjunction)
: “therefore”



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Forms of Conditional
Statements
Conditional
pq
Converse
qp
Inverse
~p~q
Contrapositive
~q~p
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Converse
Switch the hypothesis and conclusion (q  p)
pq
If two angles are vertical, then they are congruent.
qp
If two angles are congruent, then they are vertical.
Continued…..
Lesson 2-1 Conditional
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Inverse
State the opposite of both the hypothesis and
conclusion.
(~p~q)
pq : If two angles are vertical, then they are
congruent.
~p~q: If two angles are not vertical, then they are not
congruent.
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Contrapositive
Switch the hypothesis and conclusion and state
their opposites. (~q~p)
pq : If two angles are vertical, then they are
congruent.
~q~p: If two angles are not congruent, then they are
not vertical.
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More about Contrapositives

Contrapositives are logically equivalent to the
original conditional statement.

If pq is true, then qp is true.

If pq is false, then qp is false.
Lesson 2-1 Conditional
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Biconditional

When a conditional statement and its converse
are both true.

Use the phrase if and only if (sometimes
abbreviated: iff) to combine the two statements.
Statement: If an angle is right, then it has a measure of 90.
Converse: If an angle measures 90, then it is a right angle.
Biconditional: An angle is right if and only if it measures 90.
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