Transcript Conditional Statements Geometry Chapter 2, Section 1

Conditional Statements
Geometry
Chapter 2, Section 1
Notes
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Conditional Statement: is a logical statement
with two parts, a hypothesis and a conclusion.
Hypothesis: are the conditions that we’re
considering
Conclusion: is what follows as a result of the
conditions in the hypothesis.
If-then form: a style of stating a conditional
statement where the hypothesis comes
immediately after the word if and the conclusion
comes immediately after the word then.
That is, if the “if” part is satisfied then the “then”
part must follow.
Notes
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Example:
 If-then form of a conditional statement:
If it is raining outside, then the ground is
wet.
 Hypothesis – it is raining outside
 Conclusion – the ground is wet.
Notes
On your own:
 Identify the hypothesis and the conclusion, then
write the following conditional statement in if-then
form.
 A number divisible by 9 is divisible by 3
h: a number is divisible by 9
 c: it is divisible by 3
 If a number is divisible by 9, then it is divisible by 3
The 49ers will play in the Super Bowl XLII, if they win their
next game.
 h: they win their next game
 c: 49ers will play in the Super Bowl XLII
 If they win their next game then the 49ers will play in the
Super Bowl XLII
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Notes
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For a conditional statement to be true, it must be proven
true for all cases that satisfy the conditions of the
hypothesis
A single counterexample is enough to prove a conditional
statement false
 On Your Own:
 Write a counterexample to show that the following
statement is false.
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If x2 = 16, then x = 4
Counterexample: if x = -4 then x2= 16, i.e. the
hypothesis is satisfied, but x does not equal 4
This proves the statement false.
Notes
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Related Conditionals: other statements
formed by changing the original statement.
Converse: of a statement is formed by
switching the conclusion and the hypothesis.
The converse of a statement is not always
true!
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Example:
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Original: If it’s raining outside, then the ground is wet.
Converse: If the ground is wet, then it is raining outside.
Q: is the converse true or false?
False
Notes
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On Your Own: Write the converse of the following statement
 Original: If a number is divisible by 9 then it is divisible by 3
 Converse: If it is divisible by 3, then a number is divisible
by 9
 Q: is the converse true or false?
 False
 Original: If two segments are congruent, then they have the
same length.
 Converse: If two segments have the same length, then
they are congruent.
 Q: is the converse true or false?
 True
Notes
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Inverse: formed by negating the hypothesis
and conclusion of the statement
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Example
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Statement: If it’s raining outside, then the ground is wet.
Inverse: If it’s not raining outside, then the ground is not
wet.
On Your Own: write the inverse of the following
statement
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Statement: If two segments are congruent, then they have
the same length.
Inverse: If two segments are not congruent, then they do
not have the same length.
Notes
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Contrapositive: (Combination of converse
and inverse) formed by switching the
hypothesis and the conclusion and negating
them.
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Example
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Statement: If it’s raining outside, then the ground is wet.
Contrapositive: if the ground is not wet, then it is not raining
outside
On Your Own
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Statement: If two segments are congruent, then they have
the same length.
Contrapositive: If two segments do not have the same
length, then they are not congruent.
Notes
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Logically Equivalent Statements: Statements
that have the same truth value (i.e. when one is
true, so is the other)
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A statement and its contrapositive are
equivalent statements
 Original: If it’s raining outside, the ground is
wet.
 Contrapositive: If the ground isn’t wet, does
that mean it isn’t raining?
 Yes
 Lets think about this, are these two saying
the same thing?
The converse and inverse are also logically
equivalent.
Conditional Statement Activity
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Come up with your own conditional statement in
if-then form
Write the converse, inverse, and contrapositive.
Judge the validity of all four statements.
Do the equivalent statements match up as they
should and make sense?
Write counterexamples for the statements you
think are false.
Be sure to:
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Label the four statements,
Indicate whether each is true or false, and
Show which statements are equivalent to each other.
Point, Line, and Plane
Postulates
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