This document discusses conditional statements and their analysis. It defines conditional statements as logical statements written in if-then form with a hypothesis and conclusion. It explains how to determine if a conditional statement is true or false by considering the converse, inverse, and contrapositive. Conditional statements can be used to write definitions. Biconditional statements can be used when the conditional statement and its converse are both true. The document provides homework problems for students to practice these concepts.

1. 2.2 Conditional Statements
September 01, 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. 82 #3­5,
7­15,
31 & 32 1

2. 2.2 Conditional Statements
September 01, 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. 82 #3­5,
7­15,
31 & 32 2

3. 2.2 Conditional Statements
September 01, 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.
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
If A is not obtuse, then m A ≠ 99.
T
HW pg. 82 #3­5,
7­15,
31 & 32 3

4. 2.2 Conditional Statements
September 01, 2011
HW: pg. 82
#3-5,7-15,31 & 32
HW pg. 82 #3­5,
7­15,
31 & 32 4

5. 2.2 Conditional Statements
September 01, 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. 82 #3­5,
7­15,
31 & 32 5

6. 2.2 Conditional Statements
September 01, 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. 82 #3­5,
7­15,
31 & 32 6

7. 2.2 Conditional Statements
September 01, 2011
HW pg. 82 #3­5,
7­15,
31 & 32 7

8. 2.2 Conditional Statements
September 01, 2011
HW pg.83
#16-25
HW pg. 82 #3­5,
7­15,
31 & 32 8