$100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements...

52

TAGS:

Transcript of $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements...

Page 1: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.
Page 2: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

$100 $100 $100 $100 $100

$200

$300

$400

$500

$200 $200 $200 $200

$300 $300 $300 $300

$400 $400 $400 $400

$500 $500$500 $500

Inductive Reasoning and Logic

Conditional Statements

Angle and Segment Addition

Deductive Reasoning

Postulates and Proof

Page 3: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Inductive Reasoning and Logic for $100

Define: Inductive Reasoning

Page 4: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Inductive Reasoning: Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction

Back

Page 5: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Inductive Reasoning and Logic for $200

Define: Conjecture

Page 6: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Conjecture: An educated guess based on known information

Back

Page 7: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Inductive Reasoning and Logic for $300

Fill in the blanks:The _______ of a statement

is whether a statement is true or false. A statement is false if one __________ can be found.

Page 8: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

The Truth Value of a statement is whether a statement is true or false. A statement is false if one Counterexample can be found.

Back

Page 9: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Inductive Reasoning and Logic for $400

Write a logical statement using a disjunction and a negation

Page 10: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

~PvQ

Back

Page 11: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Inductive Reasoning and Logic for $500

Draw a truth table for the following compound statement:

(Pv~Q)^R

Page 12: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

P Q ~Q (Pv~Q) R (Pv~Q)^R

T T F T T T

T T F T F F

T F T T T T

T F T T F F

F T F F T F

F T F F F F

F F T T T T

F F T T F F

Page 13: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Conditional Statements for $100

Identify the hypothesis and conclusion in the following conditional statement:

If we are playing Jeapordy then, the students try to talk too much after questions

Page 14: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Hypothesis: We are playing Jeapordy

Conclusion: The students try to talk to much after questions

Back

Page 15: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Conditional Statements for $200

Write the following statement as a conditional in if-then form:

Studying Descartes makes students happy

Page 16: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

If students are studying Descartes, then they are happy

Back

Page 17: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Conditional Statements for $300

Determine whether or not the following statement is reversible (i.e. whether or not the converse is true). If it is, write the statement as a biconditional:

Two lines that are skew are not coplanar.

Page 18: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

No, they could be parallel.

Example of biconditional:

A triangle is a polygon with 3 sides

It is a triangle if and only if it is a polygon with three sides

Back

Page 19: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Conditional Statements for $400

What is logically equivalent to the converse of a statement?

Page 20: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

The Inverse of the same statement

Page 21: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Conditional Statements for $500

Write the conditional, converse, inverse, and contrapositive of the following statement and determine the truth value for each:

All squares are rectangles

Page 22: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

Conditional: If it is a square then it is a rectangle. True

Converse: If it is a rectangle then it is a square. False

Inverse: If it is not a square then it is not a rectangle. False

Contrapositive: If it is not a rectangle then it is not a square. True

Page 23: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Deductive Reasoning for $100

Define: Deductive Reasoning

Page 24: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Deductive Reasoning- Uses facts, rules, definitions, or properties to reach logical conclusions

Back

Page 25: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Deductive Reasoning for $200

Write the law of Detachment:

Page 26: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

If p implies q is true and p is true, then q is also true

[(p→q)^p]→q

Back

Page 27: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Deductive Reasoning for $300

Write the law of Syllogism

Page 28: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

If p implies q and q implies r are true, then p implies r is also true.

[(p→q)^(q→r)]→(p→r)

Back

Page 29: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Deductive Reasoning for $400

Use the law of detachment to draw a conclusion from the two statements given:

1)I can go to the concert if I can afford to buy a ticket

2)I can go to the concert

Page 30: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

No conclusion possible:

Conditional: If I can afford to buy a ticket, then I can go to the concert

Thus, (p→q)^q => Not the Law of Detachment: [(p→q)^p]→q

Back

Page 31: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Deductive Reasoning for $500

Use the Law of Syllogism to draw a conclusion from the two statements given:

1) If a number is a multiple of 64, then it is a multiple of 8

2) If a number is a multiple of 8, then it is a multiple of 2

Page 32: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

If a number is a multiple of 64, then it is a multiple of 2 by the Law of Syllogism

[(p→q)^(q→r)]→(p→r)

Back

Page 33: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Postulates and Proof for $100

Define:

Paragraph (Informal) Proof

Page 34: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

Paragraph (informal) Proof – A paragraph that explains why a conjecture for a given situation is true.

Page 35: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Postulates and Proof for $200

Write a Paragraph Proof showing that given that M is the midpoint of PQ, then PM MQ

Page 36: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

From the definition of midpoint of a segment, PM = MQ. This means that PM and MQ have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent. Thus PM MQ

Back

Page 37: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Postulates and Proof for $300

Write a two column proof showing that:

If AB = BC;AB =-5x+3;BC = -4+2x

Then, x = 1

Page 38: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

Statements ReasonsAB = BC; AB = -5x + 3

BC = -4 + 2xGiven

-5x + 3 = -4 + 2x Substitution+5x – 5x + 3 = -4 + 2x + 5x Addition Prop. of Equality3 = -4 + 7x Simplify3 + 4 = -4 + 4 + 7x Addition Prop. of Equality7 = 7x Simplify7/7 = (7x)/7 Division Prop. of Equality1 = x Simplifyx = 1 Symmetric Prop. of Algebra

Page 39: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Postulates and Proof for $400

Given that (5x-2)/2 = 9, write a two column proof to show that x=4

Page 40: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

Statements Reasons

(5x-2)/2 = 9 Given

2* (5x-2)/2 = 9 *2 Multiplication Prop of Equality

5x-2 = 18 Simplify

5x-2+2 = 18 + 2 Addition Prop. of Equality

5x = 20 Simplify

(5x)/5 = 20/5 Division Prop of Equality

x = 4 Simplify

Page 41: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Postulates and Proof for $500

List the 7 Axioms of Geometry

Page 42: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer1) Through any two points, there is exactly one line2) Through any three non-collinear points there is

exactly one plane3) A line contains at least two points4) A plane contains at least 3 points5) If two points lie in a plane, then the entire line

containing those points lies in that plane6) If two lines intersect, then their intersection is

exactly one point7) If two planes intersect then their intersection is

line

Back

Page 43: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Angle and Segment Addition for $100

Name the Property of congruence of angles that justifies the statement:

If Angle 1 Angle 2,

then Angle 2 Angle 1

Page 44: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Symmetric Property

Back

Page 45: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Angle and Segment Addition for $200

Name the Postulate that justifies the statement:

Given: Points A,B,C are collinear and point B lies between A and C, then

AB + BC = AC

Page 46: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Segment Addition Postulate

Back

Page 47: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Angle and Segment Addition for $300

Given that <PQR and <RQS form a linear pair, solve for x

R

7x-323x+22

PQ S

Page 48: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

7x – 32 + 3x + 22 = 180

10x – 10 = 180

10x = 190

x = 19

Back

Page 49: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Angle and Segment Addition for $400

Write a two column proof showing that if AC = 40 and points A, B,C are collinear, then x = 4

Page 50: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

AnswerStatements Reasons

AC = 40;A,B,C are Collinear

AB = 2x; BC = 6x+8

Given

AB + BC = AC Segment Addition Postulate

2x + 6x + 8 = 40 Substitution

8x + 8 = 40 Combining Like Terms/Simplify

8x + 8 – 8 = 40-8 Subtraction Prop. of Equality

8x = 32 Simplify

(8x)/8 = 32/8 Division Prop. of Equality

X = 4 Simplify Back

Page 51: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Angle and Segment Addition for $500

Given that m<PQR =7+x; m<RQS = 52 and m<PQS = 2x + 8. Find x

Page 52: $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Answer

Back

Using the Angle addition postulate:m<PQR + m<RQS = m<PQS

(7+x) + 52 = 2x + 8

x + 59 = 2x + 8

x + 51 = 2x

51 = x


Jeopardy IntroductionMeasurementDesign IReinforcementFBA $100 $200$200 $300 $500 $400 $300 $400 $300 $400 $500 $400.

Jeopardy IntroductionMeasurementDesign IReinforcementFBA $100 $200$200 $300 $500 $400 $300 $400 $300 $400 $500 $400.

$10 0 $200 $300 $400 $500 $100 $200 $300 $400 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

$10 0 $200 $300 $400 $500 $100 $200 $300 $400 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

$200 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $100 $200 $100.

$200 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $300 $400 $500 $100 $200 $100.

Hosted by Mr. Wyman 100 200 400 300 400 Scientific Thinking Scientific Attitudes Scientific Reasoning Potpourri 300 200 400 200 100 500 100.

Hosted by Mr. Wyman 100 200 400 300 400 Scientific Thinking Scientific Attitudes Scientific Reasoning Potpourri 300 200 400 200 100 500 100.

Parabolas $100 100 $300 $300 $200 200 $400 400 $500 500 $100 100 $300 300 $200 200 $400 400 $500 500 $100 100 $300 300 $200 200 $400 400 $500 500 $100.

Parabolas $100 100 $300 $300 $200 200 $400 400 $500 500 $100 100 $300 300 $200 200 $400 400 $500 500 $100 100 $300 300 $200 200 $400 400 $500 500 $100.

$100 $400 $300$200 $400 400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

$100 $400 $300$200 $400 400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

100 Cities 100 Urban Land Use Models Hierarchy of Cities 100 Types of Services 200 300 400 500 400 300 200 500 400 300 400 300 500 400 300 500 400 300.

100 Cities 100 Urban Land Use Models Hierarchy of Cities 100 Types of Services 200 300 400 500 400 300 200 500 400 300 400 300 500 400 300 500 400 300.

Abdominal Region HeadArmsLegsTorso 100 200 300 400 100 200 300 400 200 300 400 200 300 400 100.

Abdominal Region HeadArmsLegsTorso 100 200 300 400 100 200 300 400 200 300 400 200 300 400 100.

100 200 300 400 100 200 300 400 100 200 300 400 100 200 300 400 Final Jeopardy! * 100 200 300 400.

100 200 300 400 100 200 300 400 100 200 300 400 100 200 300 400 Final Jeopardy! * 100 200 300 400.

$100 $100 $100 $100 $500 $500 $500 $500 $200 $200 $200 $200 $300 300 $300 300 $300 300 $300 300 $400 400 $400 400 $400 $400 $400 $400 $500 500 $500.

$100 $100 $100 $100 $500 $500 $500 $500 $200 $200 $200 $200 $300 300 $300 300 $300 300 $300 300 $400 400 $400 400 $400 $400 $400 $400 $500 500 $500.

100 300 200 400 300 500 400 500 400 300 200 MISC.

100 300 200 400 300 500 400 500 400 300 200 MISC.

$100 $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $200 $300 $400 $500.

$100 $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $200 $300 $400 $500.

Jeopardy#2 $100 SocialStudiesRulesALLMedieval $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300.

Jeopardy#2 $100 SocialStudiesRulesALLMedieval $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300.

100 200 300 400 500 100 300 400 500 200 300 400 500 200 300 400 500 400 300 200 500.

100 200 300 400 500 100 300 400 500 200 300 400 500 200 300 400 500 400 300 200 500.

$100 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400.

$100 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400.

$100 $400 $300 $200 $400 $200 $100$100 $400 $200$200 $500$500 $300 $200 $500 $100 $300 $100 $300 $500 $300 $400$400 $500.

$100 $400 $300 $200 $400 $200 $100$100 $400 $200$200 $500$500 $300 $200 $500 $100 $300 $100 $300 $500 $300 $400$400 $500.

$500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100.

$500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100 $500 $500 $400 $400 $300 $300 $200 $200 $100 $100.

$200 $300 $400 Final Jeopardy $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400…

$200 $300 $400 Final Jeopardy $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400…

$ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200.

$ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200 200 $ 300 300 $ 400 400 $ 500 500 $ 100 100 $ 200.

$200 $300 $400 Democracy Matters Jeopardy $200 $300 $400 $200 $300 $400 $200 $300 $400 $200 $300 $400 $100 QuotesEnvironment EthicsScandals Healthcare.

$200 $300 $400 Democracy Matters Jeopardy $200 $300 $400 $200 $300 $400 $200 $300 $400 $200 $300 $400 $100 QuotesEnvironment EthicsScandals Healthcare.