1. 2.2 Biconditional Statements September 06, 2011
Bellwork
1. 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?
HW pg. 83 #16­25 1

2. 2.2 Biconditional Statements 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 pair
If 2 angles are a linear pair, then they are
supplementary.
HW: pg 82 #3-5
HW pg. 83 #16­25 2

3. 2.2 Biconditional Statements 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.
Negation: Opposite of original statement
Original: Ball is red.
Negation: Ball is not red.
Conditional Statement: If m A = 99, then A is obtuse.
T
Converse: exchange the hypothesis and conclusion
If m A is obtuse, then m A = 99.
F
Inverse: negate both the hypothesis and conclusion
If m A ≠99, then A is not obtuse.
F
Contrapositive: write the converse, then negate both hypothesis
and conclusion
T
If A is not obtuse, then m A ≠ 99.
HW pg. 83 #16­25 3

4. 2.2 Biconditional Statements September 06, 2011
HW: pg. 82
#3-5,7-15,31 & 32
HW pg. 83 #16­25 4

5. 2.2 Biconditional Statements 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
HW pg. 83 #16­25 5

6. 2.2 Biconditional Statements 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
HW pg. 83 #16­25 6

7. 2.2 Biconditional Statements September 06, 2011
HW pg. 83 #16­25 7

8. 2.2 Biconditional Statements September 06, 2011
HW pg.83
#16-25
HW pg. 83 #16­25 8