2.2 Conditional Statements
September 17-20, 2010
Bell Ringers - Sept 17
1. Describe the pattern in the numbers. Write the next
number in the pattern. 3, 12, 48, 192,...
2. Describe the pattern in the numbers. Write the next
three numbers in the pattern. 2, 3/2, 4/3, 5/4,...
3. If 13x +11 and 5x ­- 11 are complementary angles,
then x = ?
2.2 Conditional Statements
September 17-20, 2010
2.2 Analyze Conditional Statements
Conditional statement – a logical statement that has a
hypothesis and conclusion.
*Can be written in if-then form:
If hypothesis then conclusion.
hypothesis
p
q
"If p then q"
If it is raining, then there are clouds outside.
conclusion
Example 1: Rewrite in if-then form.
You can go to the game if you clean your room.
If you clean your room, then you can go to the game.
All birds have feathers.
If it is a bird, then it has feathers.
Guided Practice 1–3:
1. All 90º angles are right angles.
If its a right angle then its measure is 90º
2. When x = 3, x3 = 27.
If x=3 then x3=27
3. Tourists at the Alamo are in Texas.
If you are at the Alamo,
then your in Texas
2.2 Conditional Statements
September 17-20, 2010
Related Conditionals
Negation of a statement – negative of a
"opposite"
Example 2: Negate the statement
a. The book was old. The book
b. The pen is not red.
statement
was not old
The pen is red.
Verifying Statements: Conditional statements can be true or false.
To show that a conditional statement is true,
To show that a conditional statement is false,
Converse –
exchange hypothesis and conclusion
cond. statement: If hyp, then concl.
converse: If concl., then hyp.
Example 3: Write the converse of the following conditional statement.
Violin players are musicians
c.s.: If you play the violin, then you are a musician
converse: If you are a musician then you play the violin
Inverse – take the negation of both the hyp. and concl.
* If ~hyp then ~conclusion
~ means "not"
Example 4: Write the inverse of the conditional statement above.
If you do not play the violin,
then you are not a musician
3
2.2 Conditional Statements
September 17-20, 2010
To write the contrapositive,
Example 5: Write the contrapositive of the conditional statement
above.
Conditional statement: If m∠A = 99º, then ∠A is obtuse
Converse: If ∠A is obtuse, then m∠A = 99º
Inverse: If m∠A ≠ 99º, then ∠A is not obtuse.
Contrapositive: If ∠A is not obtuse, then m∠A ≠ 99º
Guided Practice:
Write the converse, inverse, and contrapositive of the following
statements.
1. If a dog is a Great Dane, then it is large.
converse: If a dog is large, then it is a Great Dane.
Inverse: If a dog in not a Great Dane, then it is not large.
contrapositive: If a dog is not large, then it is not a Great
Dane.
2. If a polygon is equilateral, then it is a regular polygon.
converse: If a polygon is regular, then it is equilateral.
inverse: If a polygon is not equilateral, then it is not a
regular polygon
contrapositive: If a polygon is not regular, then it is not
equilateral.
2.2 Conditional Statements
September 17-20, 2010
Bell Ringers - Sept 20
1. ∠TUV and ∠VUW are supplementary angles.
If m∠TUV = 4x+20 and m∠VUW = 3x - 8, find m∠TUV
and m∠VUW.
2. ∠FGH is a right angle.
Find the m∠JGH.
2)º
• J
(4x
-1
F•
3. Use the Segment Addition
Postulate to find the CD and DE.
Is D the midpoint?
CE = 113
(2x+24)º
G
•
H
C
3x + 16
•
D
6x - 20
E
4. Write the converse, inverse, and contrapositive of the following
conditional statement.
If an angle measures 90º, then it is a right angle.
2.2 Conditional Statements
Definitions can be written as conditional statements.
Perpendicular lines:
September 17-20, 2010
l
m
This definition can also be written as its converse:
Biconditional statements: When a conditional statement and
its converse are both true, you can write them as a single
biconditional statement.
biconditional statement –
Example 6: Write the definition of perpendicular lines as a
biconditional statement
Homework:
Pages 82 - 85 # 2, 4 - 10, 16, 18, 19 - 29 odd.