Download 2-2 and 2-3

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Adv Geometry
2-2 Logic and 2-3 Conditional Statements
Warm Up
State whether the following conjecture is true or false based on the given
information.
Given: n is a real number
2
Conjecture: n is a nonnegative number
2-2 Logic
 Statement – either true or false, not both
 Truth value – whether it is true or false
We usually represent statements by letters.
p, q, and r
Negation
 Opposite meaning AND opposite truth value
Example:
p: 𝒙 + 𝟐 = 𝟓
~p: 𝒙 + 𝟐 ≠ 𝟓
Combining Statements
Joining two statements with the word “and” is called a “conjunction.”
p: Lines 𝒏 and 𝒎 are parallel.
q: ∠𝑨 and∠𝑩 are adjacent angles.
Conjunctions are only true when BOTH statements are true.
Determine the truth value of the following:
𝒑^𝒒
~𝒑^𝒒
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Adv Geometry
2-2 Logic and 2-3 Conditional Statements
Example:
p: Parallel lines have congruent alternate interior angles.
q: -5 + 11 = -6
r: A triangle has 3 sides
p^q
~q ^ r
Disjunctions
 Joining statements by “or”
True - if at least one statement is true
False - if none are true
Example:
p: 100  5  20
q: The length of the radius of a circle is two times the diameter.
r: The sum of the measures of the legs of a right triangle equal the measure of
the hypotenuse.
1.)
pq
2.)
qr
2-3 Conditional Statements
A conditional statement can be written in “if-then” form.
Example:
If two lines are parallel, their corresponding angles are congruent.
We use the symbol
(Read it as “p implies q” or
“if p then q”)
p: hypothesis q: conclusion
pq
Example:
If points A, B, and C lie on a line then they are collinear.
Hypothesis:
Conclusion:
Name ______________________________ Date _________________ Period ________
Adv Geometry
2-2 Logic and 2-3 Conditional Statements
Rewriting Statements
Sometimes statements don’t have the words “if” and “then.”
We can rewrite them by first identifying the hypothesis and conclusion.
Rewrite the statement in “if-then” form:
An angle with a measure greater than 90 is an obtuse angle.
Hypothesis:
Conclusion:
Example:
If a polygon has six sides, it is called a hexagon.
Truth Values
The hypothesis, conclusion and conditional statement itself can each
have different truth values depending on different situations.
Related Conditionals
Definition: other statements based on an original conditional statement
Converse: switching the hypothesis and conclusion
Inverse: negation of BOTH the hypothesis and conclusion of original
Contrapositive: negation of the converse
Example:
Name ______________________________ Date _________________ Period ________
Adv Geometry
2-2 Logic and 2-3 Conditional Statements
Example: Write the conditional statement in if-then form. Then write the
converse, inverse, contrapositive and determine the truth values of each.
Vertical Angles are congruent.
Logically Equivalent
Statements with the same truth values are said to be logically
equivalent.
Class Work
p. 88 #13 – 23 odds
p. 94 #1-10
Homework
p. 87 #1-6
p. 95 # 27 – 36