Geometry Honors

CONDITIONAL STATEMENTS

PARTNER CHALLENGE

Amy, Bob and Carla are in a band. One is the drummer, one is the guitarist, and one is the keyboard player. Use the clues to find the instrument that each plays.Instrument Amy Bob Carl

a

DrumsGuitarKeyboard

PARTNER CHALLENGE

Instrument Amy Bob Carla

DrumsGuitarKeyboard•Carla and the drummer wear different-

colored shirts.•The keyboard player is older than Bob.•Amy, the youngest band member, lives next door to the guitarist.

Vocabulary

Conditional Statement – an if-then statement

Example:

If you are not completely satisfied,

then your money will be refunded.

Vocabulary

hypothesis– the part of the conditional statement following “if”.

Example:If you are not completely satisfied, then your money will be refunded.

Vocabulary

conclusion– the part of the conditional statement following “then”.

Example:If you are not completely satisfied, then your money will be refunded.

Your Turn:

Identify the hypothesis and the conclusion of the following conditional statement.

If y – 3 = 5, then y = 8.

Your Turn:

Write the following sentence as a conditional statement.

An integer that ends with a zero is divisible by 5.

Your Turn:

Write the following sentence as a conditional statement.

A square had four congruent sides.

Vocabulary

Truth value– determining if the conditional statement is TRUE or FALSE.

A conditional statement is TRUE if every time the hypothesis is true, the conclusion is also true.

Example of a true conditional statement: If a figure is a square, then it has four congruent sides.

Vocabulary

Truth value– determining if the conditional statement is TRUE or FALSE.

A conditional statement is FALSE if you can find just one counterexample for which the hypothesis is true and the conclusion is false.

Example of a false conditional statement: If you go to Wallenpaupack Area HS, then you live in Hawley, PA.

Your Turn:

Determine the truth value of the following conditional statement.

If you live in Philadelphia, then you live in Pennsylvania.

Your Turn:

Determine the truth value of the following conditional statement.

If a quadrilateral has four right angles, then the quadrilateral is a square.

Vocabulary

Venn Diagram– a diagram made up of overlapping circles/ovals.

A Venn Diagram can be useful in determining the truth value of a conditional statement.

Venn Diagram to represent a TRUE conditional statement.

If you are legally driving, then you are at least 16 years old.

Legal Drivers

16 year olds

Venn Diagram to represent a FALSE conditional statement.

If you play the flute, then you are in the band.

Flute Players

Band Members

Vocabulary

Converse of a Conditional Statement– switch the hypothesis and the conclusion.Example:

Conditional Statement:If 2 lines are not parallel and do not intersect, then they are skew.

Converse:If 2 lines are skew, then they are not parallel and do not intersect.

Conditional Statement:If 2 lines are not parallel and do not intersect, then they are skew.

Converse:If 2 lines are skew, then they are not parallel and do not intersect.

True or False

True or False

Conditional Statement:If a figure is a square, then it has four sides.

Converse:If a figure has four sides, then it is a square.

True or False

True or False

Symbolic Form

Conditional Statement– if p, then q.p q

Converse– if q, then p.q p

HOMEWORK

pg. 71: 1-31 odd, 43-48, 54-58.

Logic and Sudoku

2

22

2

2

1

11

1

1

11

3

3

33

3

33

4

44

4

44

4

5

55

5

5

6

6

6

6

6

6

7

77

7

7

7

8

8

8

88

89

9

9

9

99

9

9

Vocabulary

Biconditional Statement – a statement you get by connecting the conditional statement and its converse with the word “and”.

You can also use the phrase “if and only if”.Can only be combined if the conditional statement and its converse are both true.

Example of a Biconditional:Conditional Statement:

If two angles have the same measure, then the angles are congruent.

Converse:If two angles are congruent, then the angles have the same measure.

Biconditional:Two angles have the same measure if and only if the two angles are congruent.

Since both the conditional and converse statements are true…

Symbolic Form

Conditional Statement– if p, then q.p q

Converse– if q, then p.q p

Biconditional– p if and only if qp q

What makes a Good Definition?

Uses clearly understood terms

Precise (don’t use words such as sort of, or some)Reversible (can be written as a biconditional)

Is this a Good Definition?

A right angle is an angle whose measure is 90.

Biconditional: An angle is a right angle if and only if its measure is 90.

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

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

Good Definition

Is this a Good Definition?

An airplane is a vehicle that flies.

Counterexample: A helicopter is a vehicle that flies.

Conditional: If its an airplane, then it’s a vehicle that flies.

Converse: If it’s a vehicle that flies, then it is an airplane.

Bad Definition

HOMEWORK

pg. 78: 1-23, 27, 32-35.

PARTNER CHALLENGE

Alan, Ben, and Cal are seated as shown with their eyes closed. Diane places a hat on each of their heads from a box that contains 3 red hats and 2 blue hats. They open their eyes and look forward. Alan says, “I cannot deduce what color hat I’m wearing.” Hearing that, Ben says, “I cannot deduce what color hat I’m wearing either.” Cal then says, “I know what color I am wearing.” What color is Cal’s hat? How does Cal know the color of his hat?

Alan Ben Cal

Vocabulary

Negation– having the opposite truth value.

Example of Negation:

Statement: I studied 4 hours.Negation: I did not study 4

hours.Statement: I do not like reading books.

Negation: I like reading books.

Symbolic Form

~

VocabularyInverse of a Conditional Statement– negation of both the hypothesis and the conclusion.

Conditional Statement:If two angles have the same measure, then the angles are congruent.

Inverse:If two angles do not have the same measure, then the angles are not congruent.

Vocabulary

Contrapositive of a Conditional Statement– switches the hypothesis and the conclusion and negates both.

Conditional Statement:If a figure is a square, then it is a rectangle.

Contrapositive:If a figure is not a rectangle, then it is not a square.

Switch and negate both

Symbolic Form

Conditional Statement– if p, then q.p q

Negation– not p~p

Inverse– If not p, then not q~p ~q

Contrapositive– If not q, then not p~q ~p

Conditional StatementIf a person is old enough to vote, then he/she is at least 18 years old.Converse

If a person is at least 18 years old, then he/she is old enough to vote.InverseIf a person is NOT old enough to vote, then he/she is NOT at least 18 years old.ContrapositiveIf a person is at NOT least 18 years old, then he/she is NOT old enough to vote.

p q

q p

~p ~q

~q ~p

Biconditional StatementA person is old enough to vote, if and only if he/she is at least 18 years old.

HOMEWORK

pg. 267: 1-9, 22-27, 33-35, 42-44

Logic and Sudoku

2

22

2

2

1

11

1

1

11

3

3

33

3

33

4

44

4

44

4

5

55

5

5

6

6

6

6

6

6

7

77

7

7

7

8

8

8

88

89

9

9

9

99

9

9

Possible Hat Combinations:

Alan

Ben Cal

R R RR R BR B RR B BB R RB R BB B R

Alan would know what he was wearing if he saw two blue hats in front of him.

If Ben saw blue, he new that he was wearing red. Therefore, he did not see blue.

Therefore, Cal must be wearing red.