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Kevin M. Bond, PHD

Geometry: Week 5

Monday: Exam 1a Debrief

Tuesday: Exam 1b

Wednesday: 2.1 – Conditional Statements

Thursday: 2.2 – Definitions and

Biconditional Statements

Friday: 2.2 – Work Day

Next Week

• 2.3, 2.4, 2.5

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Kevin M. Bond, PHD

Monday: Mindfulness Training

This week: working with difficulty

http://marc.ucla.edu/mpeg/04_Meditation_for_Wor

king_with_Difficulties.mp3

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Kevin M. Bond, PHD

Debrief Exam 1a

Review definitions

Work page 64, “Chapter Standardized Test”

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Kevin M. Bond, PHD

Tuesday: Mindfulness Training

STOP Meditation

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Kevin M. Bond, PHD

Exam 1b Day

.

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Kevin M. Bond, PHD

Wednesday:

Mindfulness Training

This week: working with difficulty

http://marc.ucla.edu/mpeg/04_Meditation_for_Wor

king_with_Difficulties.mp3

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Perry High School

Kevin M. Bond, PHD

Starting Chapter 2

Reasoning and Proof

• Basis of reliable

knowledge

• Foundation of computer

programming

2.1: Conditionals

1 DAY!

Homework:

Due when class starts

Tomorrow

Guided Practice: p., 75, 1-8

Practice and Applications

p., 75, 10-50 odd

51, 55, 56, 64, 68, 74

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Kevin M. Bond, PHD

Statements

Statements – a.k.a. a claim – a sentence that is

either true or false, but not both.

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Kevin M. Bond, PHD

Statements

Statements – a.k.a. a

claim – a sentence that

is either true or false,

but not both.

• The following are

statements

– It is raining.

– The moon is made of

cheese.

– Five plus three is eight.

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Kevin M. Bond, PHD

Statements

Statements – a.k.a. a

claim – a sentence that

is either true or false,

but not both.

• The following are

statements

– It is raining.

– The moon is made of

cheese.

– Five plus three is eight.

• Not statements

– Dag nabbit!

– 5 o’clock

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Kevin M. Bond, PHD

Parts of Conditionals

Conditional Statements have two parts:

1. Hypothesis – gives some condition

Usually represented by an “IF”

2. Conclusion -- tells us what happens

Usually represented by a “THEN”

Example: If we meditate, then we grow brain tissue.

Hypothesis: We meditate

Conclusion: We grow brain tissue

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Kevin M. Bond, PHD

Working with Conditionals

Identify the hypothesis

and the conclusion

1. If you want good

service, then you

take your car to

Joe’s AAA.

2. If you like tennis,

then you play on the

tennis team.

Rewrite as if-then

conditional

3. Today is Monday if

yesterday was

Sunday.

4. A number is divisible

by 4 if it is divisible

by 8.

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Kevin M. Bond, PHD

Counterexample, redux

Counterexample – an

example that shows

something is false.

To show a statement is

false, you use a

counterexample.

Find counterexamples

1. If x2=16, then x=8.

2. A point may lie on at

most two lines.

3. Dr. Bond does not

wear glasses.

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Kevin M. Bond, PHD

Converse

Converse – the converse of a statement is formed

by switching the hypothesis and conclusion.

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Kevin M. Bond, PHD

Converse

Converse – the converse of a statement is formed

by switching the hypothesis and conclusion.

Statement: If you don’t blink, then you will be okay.

Converse: If you are okay, then you don’t blink.

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Kevin M. Bond, PHD

Converse

Converse – the

converse of a

statement is formed

by switching the

hypothesis and

conclusion.

Statement: If it rains,

then the grass is wet.

Converse: If the grass

is wet, then it rained.

Statement: If I am

quick, I should play

basketball.

Converse: ???

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Kevin M. Bond, PHD

Converse

Converse – the

converse of a

statement is formed

by switching the

hypothesis and

conclusion.

Statement: If it rains,

then the grass is wet.

Converse: If the grass

is wet, then it rained.

Statement: If I am

quick, I should play

basketball.

Converse: If I play

basketball, then I am

quick.

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Kevin M. Bond, PHD

Negation

• Negation – the negative of a statement

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Kevin M. Bond, PHD

Negation

Negation – the

negative of a statement

Statement: I am tall

Negation: I am not tall

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Kevin M. Bond, PHD

Negation

Negation – the

negative of a statement

Statement: I am tall

Negation: I am not tall

Statement: Fish can

swim.

Negation: ???

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Kevin M. Bond, PHD

Negation

Negation – the

negative of a statement

Statement: I am tall

Negation: I am not tall

Statement: Fish can

swim.

Negation: Fish can not

swim.

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Kevin M. Bond, PHD

Inverse

Inverse-when you negate the hypothesis and

conclusion of a conditional statement.

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Kevin M. Bond, PHD

Inverse

Inverse-when you

negate the hypothesis

and conclusion of a

conditional statement.

Statement: If it rains,

then the grass is wet.

Inverse: If it does not

rain, then the grass is

not wet.

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Kevin M. Bond, PHD

Contrapositive

Contrapositive – the inverse of the converse of a

conditional statement; when you negate the hypothesis and

conclusion of the converse of a conditional statement.

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Kevin M. Bond, PHD

Contrapositive

Contrapositive – the inverse of the converse of a conditional

statement; when you negate the hypothesis and conclusion

of the converse of a conditional statement.

Statement: If it rains, the grass is wet.

Converse:

Contrapositive:

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Perry High School

Kevin M. Bond, PHD

Contrapositive

Contrapositive – the inverse of the converse of a conditional

statement; when you negate the hypothesis and conclusion

of the converse of a conditional statement.

Statement: If it rains, the grass is wet.

Converse: If the grass is wet, then it rains.

Contropositive: If the grass is not wet, then it did

not rain.

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Kevin M. Bond, PHD

Equivalent Statements

Equivalent – has the

same truth value.

Original statements and

their contropositives

are equivalent.

Inverse and converse

statements are

equivalent.

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Kevin M. Bond, PHD

Recall: Postulates

• Ruler Addition Postulate

• Segment Addition Postulate

• Protractor Postulate

• Angle Addition Postulate

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Kevin M. Bond, PHD

2.1 Postulates, p. 73

• Postulate 5: Through any two points there

exists exactly one line.

• Postulate 6: A line contains at least two points.

• Postulate 7: If two distinct lines intersect, then

their intersection is exactly one point.

• Postulate 8: Through any three noncollinear

points there exists exactly one plane.

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Kevin M. Bond, PHD

2.1 More Postulates, p. 73

• Postulate 9: A plane contains at least three

noncollinear points.

• Postulate 10: If two points lie on a plane, then

the line containing them lies in the plane.

• Postulate 11: If two planes intersect, then their

intersection is a line.

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Kevin M. Bond, PHD

2.1 Work

Due when class starts Tomorrow

Guided Practice

Page 75, 1-8 all

Practice and Applications

Page 75

10-50 odd (check your work!)

51, 55, 56, 64, 68, 74

Show Instructor When Finished

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Perry High School

Kevin M. Bond, PHD

Thursday:

Mindfulness Training

This week: working with difficulty

http://marc.ucla.edu/mpeg/04_Meditation_for_Wor

king_with_Difficulties.mp3

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Perry High School

Kevin M. Bond, PHD

Debrief 2.1

Questions on

Practice and Applications?

Spot Check While Reading 2.2

Mixed Review p. 78: Evens

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Kevin M. Bond, PHD

2.2 Definitions / Biconditionals

Note: 2 Days

Checking work on Day 2

Day One

• Lecture

• Guided Practice

• HW

• -- Mixed Review

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Kevin M. Bond, PHD

Goals

• Use definitions to

justify claims.

• More generally, this is

part of using

foundational

knowledge to justify

how you know things.

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Kevin M. Bond, PHD

Perpendicular

Perpendicular Lines –

Two lines are

perpendicular if they

intersect to form a

right angle.

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Kevin M. Bond, PHD

Line Perpendicular to Plane

A line is perpendicular

to a plane if the line

intersects the plane in

a point and is

perpendicular to

every line in the plane

that intersects it.

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Kevin M. Bond, PHD

Only-If

“only-if” is a pseudo-

form of a conditional

statement, it’s a

conditional but

“backwards.”

It rains only if the grass

is wet.

Warning: Looks like it

should be “if the grass

is wet, then it rained.”

NO!

It turns into, “If it rains,

then the grass is wet.”

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Perry High School

Kevin M. Bond, PHD

Only-If

• Only if I go to the movies then I’ll meet

you.

– Translate: ???

• I ate too much pie only if my stomach

hurts.

– Translate: ???

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Kevin M. Bond, PHD

Only-If

• Only if I go to the movies then I’ll meet

you.

– Translate: If I meet you, then I go to the

movies.

• I ate too much pie only if my stomach

hurts.

– Translate: If I ate too much pie, then my

stomach hurts.

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Kevin M. Bond, PHD

Biconditional Statements

• “If and only if” aka “iff”

• A “two direction” conditional statement

• A conditional statement and it’s converse joined

together

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Kevin M. Bond, PHD

Biconditional Statements

• “If and only if” aka “iff”

• A “two direction”

conditional statement

• A conditional

statement and it’s

converse joined

together

• Two segments are

congruent if and only

if they have the same

measure.

• You may go to the

movies Friday night if

and only if you clean

your room.

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Perry High School

Kevin M. Bond, PHD

2.2, Day 1

Guided Practice

Page 82, 1-12

Page 85, 59-68

By end of class on day 2

Page 82+

32–44 all

46, 50–55

Show Instructor When

Completed

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Perry High School

Kevin M. Bond, PHD

Friday: Mindfulness Training

This week: working with difficulty

http://marc.ucla.edu/mpeg/04_Meditation_for_Wor

king_with_Difficulties.mp3

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Perry High School

Kevin M. Bond, PHD

2.2 Work Day

Page 82+

32–44 all

46, 50–55

Show Instructor When

Completed

Next Week: 2.3, 2.4, 2.5