•4.4:

• Analyze Conditional Statements

Vocabulary:a_______________________ is a logical statement that has two parts, a hypothesis and a conclusion. When it is written in an “if-then form”,

the “if” part is the _______________ and the “then” part is the _____________

Example: circle the whether or not the underline phrase is the hypothesis or conclusion.

If I water my flowers, then they will grow(hypothesis/conclusion) (hypothesis/conclusion)

You try:If I study for my test, then I will do better on my test.

(hypothesis/conclusion) (hypothesis/conclusion)__________________:when you switch the hypothesis and the

conclusion __________________: when you negate (say opposite of) the

hypothesis and conclusion._________________: when you switch the hypothesis and conclusion

AND negate them.

Rewrite the statement in if-then format.

1. All sharks have a boneless skeleton.

2. When n = 6, n² = 36.

6n

1. If it is a shark, then it has a boneless skeleton .

2. If n = 6, then n² = 36.

Write If-then form, converse, inverse, and contrapositive, and determine if each is true or false.

Basketball players are athletes.

If-then:

Converse:

Inverse:

Contrapositive:

• If-then: If they are basketball players, then they are athletes.

• Converse: If they are athletes, then they are basketball players.

• Inverse: If they are NOT basketball players, then they are NOT athletes.

• Contrapositive: If they are NOT athletes, then they are NOT basketball players.

True or False?

• Vocabulary:

• If 2 lines intersect to form right angles, they are _______________ lines

• When a statement and its converse are BOTH true, you can write them as a __________________________ statement. This statement contains “_____________”

Write a BICONDITIONAL

• If a polygon is equilateral, then all of its sides are congruent.

• Converse:

• Biconditional:

• Converse: If all of the sides are congruent, then it is an equilateral polygon

• BICONDITIONAL: A polygon is equilateral if and only if all of its sides are congruent.

• 4.4: Apply Deductive Reasoning (note: different than logic in 4.2: Inductive Reasoning)

• Vocabulary:• ____________________ reasoning uses facts,

definitions, accepted properties, and logic to form logical argument.

• ___________________________ if the hypothesis is true, then the conclusion is true– If p, then q– P, therefore q

• ___________________________ – If p, then q– If q, then r– P, therefore r

Law of Detachment:

• Example:

• If you order desert, then you will get ice cream

• Sarah ordered desert

• Sarah got ice cream

• Example:

• If you run every day, then you will be in good shape.

• Ms. Towner runs every day

• Ms. Towner is in good shape.

• Example:

• If is angle A is acute, then angle A is less than 90 degrees.

• Angle B is acute.

• Angle B is less than 90 degrees.

You Try:

• If an angle measures more than 90 degrees, then it is not acute.

• The measure of angle ABC is 120 degrees.

• Angle ABC is not acute.

You Try:

• If two lines will never intersect, then they are parallel

• Lines AB and CD never intersect.

• Lines AB and CD are parallel.

Law of Syllogism:

• Example:

• If you wear school colors, then you have school spirit

• If you have school spirit, then your team feels great.

• If you wear school colors, then your team feels great

• Example:

• If you study hard, then you will do well in your classes.

• If you do well in your classes, then you will graduate.

• If you study hard, then you will graduate.

• Example:

• If angle 2 is acute, then angle 3 is obtuse.

• If angle 3 is obtuse, then angle 4 is acute.

• If angle 2 is acute, then angle 4 is acute.

You Try:

• If a=bd, then c=fd

• If c=fd, then d=oh

• If a = bd, then d = oh.

You Try:

• If jlt, then pql

• If pql, then jtw

• If jlt, then jtw.

Use Inductive and deductive reasoning:

• Example: Make a conclusion about the sum of 2 even integers.

• STEP 1: Inductive Reasoning• Pick a few samples: -2+4=2 ; 8+6=14• Conjecture: even# + even # = even#• STEP 2: Deductive Reasoning• Use logic to prove your conjecture

(first write a ‘let’ statement• Let n and m equal any integer

PROOF• 2n is even; 2m is even

• 2n+2m is the sum of even numbers

• 2n+2m= 2(n+m)• 2(n+m) is even

• 2(n+m) was the sum of

2n+2m• even #+even# = even #

REASON• b/c multiplying by 2

makes it an even number• Addition

• factoring• b/c multiplied by 2 makes

an even number• 3rd bullet 2n+2m=2(n+m)

• b/c 2n is even, 2m is even, 2(n+m) is even, and 2n+2m=2(n+m)