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2.2 Biconditional Statements
HW pg. 83 #1625 1
September 06, 2011
Bellwork1. What is the definition of conjecture? A guess based on observation
2. Write the next number in the sequence 1, 5, 9, 13,... 17
3. A _______ disproves a conjecture. counterexample
4. (4)(7)+2 1=? 27
5. Are you lost yet in chapter 2?
2.2 Biconditional Statements
HW pg. 83 #1625 2
September 06, 2011
2.2 Analyze Conditional Statements
Conditional Statement:
logical statement that has 2 parts-
hypothesis & conclusion
written in if-then form
Ex. If it is raining, then there are clouds in the sky.
Rewrite the conditional statement in if-then form.
All birds have feathers.If an animal is a bird, then it has feathers.
2 angles are supplementary if they are a linear pairIf 2 angles are a linear pair, then they are
supplementary.
HW: pg 82 #3-5
2.2 Biconditional Statements
HW pg. 83 #1625 3
September 06, 2011
• Conditional statements can be T or F.
• Prove that the conclusion is true every time the hypothesis is true.
• To show false: give 1 counterexample.
Conditional Statement: If m A = 99, then A is obtuse.
Converse: exchange the hypothesis and conclusionIf m A is obtuse, then m A = 99.
Inverse: negate both the hypothesis and conclusionIf m A ≠99, then A is not obtuse.
Contrapositive: write the converse, then negate both hypothesis and conclusionIf A is not obtuse, then m A ≠ 99.
T
F
T
F
Negation: Opposite of original statementOriginal: Ball is red.Negation: Ball is not red.
2.2 Biconditional Statements
HW pg. 83 #1625 4
September 06, 2011
HW: pg. 82
#3-5,7-15,31 & 32
2.2 Biconditional Statements
HW pg. 83 #1625 5
September 06, 2011
You can write a definition as a conditional statement in if-then form or as its converse. Both are True.
Definition: If 2 lines intersect to form a right angle, then they are perpendicular lines.
Converse: If 2 lines are perpendicular, then they intersect to form a right angle.
You can write "line l is perpendicular to line m" as l m.
l
m
HW pg. 83 #16-18
2.2 Biconditional Statements
HW pg. 83 #1625 6
September 06, 2011
Biconditional Statement: • When conditional statement and converse are T, then
you can write them as a biconditional statement.
• if and only if (IFF)
• any valid definition can be written as biconditional
2.2 Biconditional Statements
HW pg. 83 #1625 7
September 06, 2011
2.2 Biconditional Statements
HW pg. 83 #1625 8
September 06, 2011
HW pg.83
#16-25
