Do Now:

1. Copy Down HW.

2. Describe the pattern, then find the next two numbers in the pattern:

3, 12, 48, 192, …

2.2Conditional Statements

5 cards

Conditional Statements:

A fact written as “If, Then”

If = Hypothesis

Then = Conclusion

Ex 1: Identify the Hypothesis and the Conclusion

• If Varsity wins the game, then they go to the finals.

• If two lines are parallel, then the lines are coplanar.

• If x – 6 = 4, then x = 10

Ex 1: Identify the Hypothesis and the Conclusion

• If Varsity wins the game, then they go to the finals.

• If two lines are parallel, then the lines are coplanar.

• If x – 6 = 4, then x = 10

Ex 2: Write a Conditional • An acute angle measures less than 90

degrees.If an angle is acute, then it measures less than

90 degrees.• An Integer that ends with 0 is divisible by 5.If an integer ends with 0, then it is divisible by

5• A square has four congruent sides.If a figure is a square, then it has four

congruent sides.

Truth Value

True means ALWAYS true.

False means FALSE at least ONCE.

Ex 3: False Conditionals:

Give at lease one counterexample to prove the statements false.• If you are a girl, then you have long

hair.• If it is February, then there are only

28 days in the month.• If x squared is greater than 0, then x

is greater than 0.

Converse

Switch Switch Hypothesis and Hypothesis and

ConclusionConclusionNOT ALWAYS NOT ALWAYS

TRUETRUE

Ex 4: Converse ; Switch Hypothesis and ConclusionNOT ALWAYS TRUE

Conditional: If two lines are parallel, then they never intersect.

Converse: If two lines never intersect, then they are parallel

True or False? FALSE: They could be skew

Converse : Switch Hypothesis and ConclusionNOT ALWAYS TRUE

Conditional:If an angle measures 90 degrees, then it is a right

angle.

Converse: If an angle is a right angle, then it measures 90 degrees.

True or False?

Converse : Switch Hypothesis and ConclusionNOT ALWAYS TRUE

Conditional:If an angle measures 90 degrees, then it is a

right angle.

Converse: If an angle is a right angle, then it measures 90 degrees.

True

Write the Converse, Determine if the converse is True or False.

Conditional:If x = 9, then x + 3 = 12.

Converse:If x + 3 = 12, then x = 9.

True

Summary

Conditional: If a is true, then b is true.Read it “If A, then B”

A B

Converse: Switch A and B; Not always true

B A

InverseNegate the Negate the

Hypothesis and Hypothesis and ConclusionConclusion

NOT ALWAYS NOT ALWAYS TRUETRUE

Example 5: Write the inverse, Determine if the inverse is True or False. Conditional:If an animal is a whale, then it is a mammal.

Inverse:If an animal is not a whale, then it is not a mammal.

False

Conditional:If an animal is a whale, then it is a mammal.

Inverse:If an animal is not a whale, then it is not a mammal.

False

Write the inverse, Determine if the inverse is True or False.

Conditional:If a polygon is regular, then the polygon is equilateral.

Inverse:If a polygon is not regular, then the polygon is not equilateral.

False

Conditional:If a polygon is regular, then the polygon is equilateral.

Inverse:If a polygon is not regular, then the polygon is not equilateral.

False

ContrapositiveNegateNegate the the

Hypothesis and Hypothesis and Conclusion then Conclusion then

SwitchSwitch Them Them

NOT ALWAYS NOT ALWAYS TRUETRUE

Example 6: Write the Contrapositive, Determine if the contrapositive is True or False.Conditional:If you are on the Varsity Football Team, then you

wear a football jersey.

Contrapositive:If you don’t wear a football jersey, then you are not

on the Varsity Football Team.

Write the Contrapositive, Determine if the contrapositive is True or False.Conditional: If a figure is a square, then it has four right angles.

Contrapositive: If a figure does not have four right angles, then the

figure is not a square.

True

Bi-conditionalIf a conditional and If a conditional and

its converse are its converse are true, then the true, then the

statement can be statement can be written as “if and written as “if and

only if.”only if.”

Write the Bi-Conditional

Conditional: If a number is divisible by 2, then it is even.

Converse:If a number is even, then it is divisible by 2.True

Bi-Conditional:A number is divisible by 2 if and only if it is even.

Exit Slip:

Write an if, then statement that is true.

Then write the converse, inverse, and contrapositive of that statement-tell whether each of those statements are true or false.