Download Biconditional Statements

Term
Inductive
Reasoning
Conjecture
Definition
Example
Making specific observations to
arrive at an educated guess.
 Look for a pattern
 Make a conjecture
 Verify the conjecture
An educated guess.
- Made based on observations of
particular situations.
- May be true or false.
Examples: All of your friends are good.
Prediction:
Given: Everyone passed the Unit test.
Conjecture:
To prove false, you need to
provide a single counterexample.
Counterexample
An example used to show that a
conjecture is not always true.
Given: Jack went home from the nurse
yesterday and he is not in class today.
- Only one counterexample is
needed to show that a conjecture
is not true.
Conjecture:
Counterexample:
VISUAL PATTERNS: Determine the next picture in the sequence.
Figure 4
NUMBER PATTERNS: Describe the pattern in the numbers –7, -21, -63, -189, … and write the
next three numbers in the pattern.
GEOMETRIC PATTERNS: Given five collinear points, make a conjecture about the number of
ways to connect different pairs of the points.
Find a counterexample:
1.) A student makes the following conjecture about the difference of two numbers. Find a
counterexample to disprove the students conjecture:
The difference of any two numbers is always smaller than the larger number
2.) All prime numbers are odd.
3.) All odd numbers are prime.
Decide whether the statement is true or false. If false provide a counter example.
4.) If x2 = 16, then x = 4.
5.) A point may lie on at most two lines.
Conditional Statements: a logical statement with two parts, a ___________and a __________
If – Then: “if” part is the ________________and the “then” part is the ____________
Identify the hypothesis and conclusion: If the weather is warm, then we should go swimming.
hypothesis:
conclusion:
Conditional Statement ____  ____
If-Then
1) If m  A = 30, then  A is acute
Converse ____  ____
Switch the hypothesis and conclusion
True
1) If  A is acute, then m  A = 30. False
2) If you are a basketball player, then you are
an athlete.
True
2)
Inverse ____  ____
Contrapositive ____  ____
Negate the hypothesis and conclusion
Negate and Switch
1) If m  A  30, then  A is not acute. False
1) If  A is not acute, then m  A  30. True
2)
2)
Practice: Write the inverse, converse, and contrapositive of the conditional statement.
Conditional Statement: If two angles are congruent then they have the same measure.
Converse:
Inverse:
Contrapositive:
Biconditional Statements: a statement that contains the phrase
_________________:___
Biconditional Statements can be true or false
Biconditional statement is true if 1.) the __________________ is __________
2.) the __________________ is __________
Practice: Rewrite the biconditional statement as a conditional statement and its converse.
6.) Three lines are coplanar if and only if they lie in the same plane.
Conditional statement:
Converse:
Determine whether the biconditional statement is true or false.
7.) x = 3 if and only if x2 = 9
Conditional:
true or false
Converse:
true or false
Perpendicular: two lines are called perpendicular lines if they____________________ to
form a ___________ __________.
SYMBOL: _____
Definition of Perpendicular lines: If ______________________________________, then
___________________________________________________.
**Converse is also true, so it is a biconditional statement.
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