$100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates and Proof

Inductive Reasoning and Logic for $100 Define: Inductive Reasoning

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

Inductive Reasoning and Logic for $200 Define: Conjecture

Answer Conjecture: An educated guess based on known information Back

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.

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

Inductive Reasoning and Logic for $400 Write a logical statement using a disjunction and a negation

Answer ~PvQ Back

Inductive Reasoning and Logic for $500 Draw a truth table for the following compound statement: (Pv~Q)^R

Answer Back PQ~Q(Pv~Q)R(Pv~Q)^R TTFTTT TTFTFF TFTTTT TFTTFF FTFFTF FTFFFF FFTTTT FFTTFF

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

Answer Hypothesis: We are playing Jeapordy Conclusion: The students try to talk to much after questions Back

Conditional Statements for $200 Write the following statement as a conditional in if-then form: Studying Descartes makes students happy

Answer If students are studying Descartes, then they are happy Back

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.

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

Conditional Statements for $400 What is logically equivalent to the converse of a statement?

Answer Back The Inverse of the same statement

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

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

Deductive Reasoning for $100 Define: Deductive Reasoning

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

Deductive Reasoning for $200 Write the law of Detachment:

Answer If p implies q is true and p is true, then q is also true [(p→q)^p]→q Back

Deductive Reasoning for $300 Write the law of Syllogism

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

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

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

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

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

Postulates and Proof for $100 Define: Paragraph (Informal) Proof

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

Postulates and Proof for $200 Write a Paragraph Proof showing that given that M is the midpoint of PQ, then PM MQ

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

Postulates and Proof for $300 Write a two column proof showing that: If AB = BC;AB =-5x+3;BC = -4+2x Then, x = 1

Answer Back StatementsReasons AB = BC; AB = -5x + 3 BC = x Given -5x + 3 = x Substitution +5x – 5x + 3 = x + 5x Addition Prop. of Equality 3 = x Simplify = x Addition Prop. of Equality 7 = 7x Simplify 7/7 = (7x)/7 Division Prop. of Equality 1 = x Simplify x = 1 Symmetric Prop. of Algebra

Postulates and Proof for $400 Given that (5x-2)/2 = 9, write a two column proof to show that x=4

Answer Back StatementsReasons (5x-2)/2 = 9Given 2* (5x-2)/2 = 9 *2Multiplication Prop of Equality 5x-2 = 18Simplify 5x-2+2 = Addition Prop. of Equality 5x = 20Simplify (5x)/5 = 20/5Division Prop of Equality x = 4Simplify

Postulates and Proof for $500 List the 7 Axioms of Geometry

Answer 1)Through any two points, there is exactly one line 2)Through any three non-collinear points there is exactly one plane 3)A line contains at least two points 4)A plane contains at least 3 points 5)If two points lie in a plane, then the entire line containing those points lies in that plane 6)If two lines intersect, then their intersection is exactly one point 7)If two planes intersect then their intersection is line Back

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

Answer Symmetric Property Back

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

Answer Segment Addition Postulate Back

Angle and Segment Addition for $300 Given that <PQR and <RQS form a linear pair, solve for x R 7x-32 3x+22 P QS

Answer 7x – x + 22 = x – 10 = x = 190 x = 19 Back

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

Answer StatementsReasons AC = 40; A,B,C are Collinear AB = 2x; BC = 6x+8 Given AB + BC = ACSegment Addition Postulate 2x + 6x + 8 = 40Substitution 8x + 8 = 40 Combining Like Terms/Simplify 8x + 8 – 8 = 40-8Subtraction Prop. of Equality 8x = 32Simplify (8x)/8 = 32/8Division Prop. of Equality X = 4Simplify Back

Angle and Segment Addition for $500 Given that m<PQR =7+x; m<RQS = 52 and m<PQS = 2x + 8. Find x

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