Write The First Five Terms Of Two
Lesson 2.1 inductive reasoning geometry answer key. Solve the Questions available in BIM Book Geometry Chapter 2 Reasoning and Proofs Answer Key on a frequent basis and get a good hold of the concepts. Get thousands of teacher-crafted activities that sync up with the school year. 21 Inductive Reasoning 22 Conditional Statements 23 Biconditional Statements 24 Deductive Reasoning 25 Algebraic Reasoning and Proof 26 Geometric Reasoning.
Use inductive reasoning to determine the next two terms in each sequence. The headings and the Key Concept box. Ad Access the most comprehensive library of printable K-8 lesson plans.
Lesson 2-1 Inductive Reasoning Use the four circles below. 2 4 8 16 12. 5 4.
10 CHAPTER 2 Discovering Geometry Practice Your Skills 2003 Key Curriculum Press. Key Vocabulary Conjecture A conjecture is an unproven statement that is based on observations. Chapter2ReasoningandProofAnswerKeyCK512BasicGeometry Concepts121 Inductive Reasoning from Patterns Answers 1.
12 1 2 6 1 4 3. Lesson 11 Identify draw models of and use postulates about points lines and planes. Lessons 12 and 13 Write statements in if-then form and write their converses.
Mathematical Reasoning Local Standards. Common Core 15th Edition answers to Chapter 2 Reasoning and Proof 2-1 Patterns and Inductive Reasoning Practice and Problem-Solving. Describe patterns and use inductive reasoning.
_____ Lesson 1-1 Patterns and Inductive Reasoning. LESSON 2-1 PRACTICE 11. X 2 y 1 10.
Geometry Name Notes
Inductive And Deductive Reasoning
Exploration 1
Writing a Conjecture
Work with a partner: Write a conjecture about the pattern. Then use your conjecture to draw the 10th object in the pattern.a.The circle is rotating from one vertex to the next in a clockwise direction
b.Answer:The pattern alternates between a curve in an odd quadrant and a line with a negative slope in the even quadrant.
c.The pattern alternates between the first three arrangements, then their respective mirror images.
Exploration 2
Using a Venn Diagram
Work with a partner: Use the Venn diagram to determine whether the statement is true or false. Justify your answer. Assume that no region of the Venn diagram is empty.
CONSTRUCTING VIABLE ARGUMENTSTo be proficient in math, you need to justify your conclusions and communicate them to others.
a. If an item has Property B. then it has Property A.Answer:
b. If an item has Property A. then it has Property B.Answer:
c. If an item has Property A, then it has Property C.Answer:
d. Some items that have Property A do not have Property B.Answer:
e. If an item has Property C. then it does not have Property B.Answer:
f. Sonic items have both Properties A and C.Answer:
g. Some items have both Properties B and C.Answer:
Exploration 3
Reasoning and Venn Diagrams
Answer:
Question 4.Make and test a conjecture about the sign o1 the product of any three negative integers.Answer:
Make and test a conjecture about the sum of any five consecutive integers.Answer:
Exercise 22 Inductive And Deductive Reasoning
Vocabulary and Core Concept Check
Question 1.How does the prefix counter help you understand the term counterexample?Answer:Because the prefix counter means opposing, a counter example opposes the truth of the statement.
Question 2.Explain the difference between inductive reasoning and deductive reasoning.Answer:Inductive reasoning is finding a pattern in specific case and then writing a conjecture for the general case.Deductive reasoning uses facts, definitions, accepted properties and the laws of logic to form a logical argument.Inductive reasoning would be like generalizing and deductive reasoning would be like concluding.
Monitoring Progress and Modeling with Mathematics
In Exercises 3 8, describe the pattern. Then write or draw the next two numbers, letters, or figures.
Question 3.1, 2, 3, 4, 5, ..Answer:
0, 2, 6, 12, 20, ..Answer:This is sequence of numbers where first number is 0, and every next number is obtained by adding 2, 4, 6, to previous number.Next two numbers are: 30, 42
Question 5.Z, Y, X, W, V, ..Answer:
J, F, M, A, M, ..Answer:J = January, F = February, M = March, A = April, M = MayThe next two letters would be J and JJ = June, J = July
The quotient of two negative integers is positive rational number.
In Exercises 13 16, find a counter example to show that the conjecture is false.
Question 13.The product of two positive numbers is always greater than either number,Answer:
Question 29.the sum of two odd integersAnswer:
Question 47.
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Lesson 24 Deductive Reasoning
1. ABC is equilateral. Is ABD equilateral? Explain your answer.
What type of reasoning, inductive or deductive, do you use when
solving this problem?
2. A and D are complementary. A and E are supplementary.
What can you conclude about D and E? Explain your answer.
What type of reasoning, inductive or deductive, do you use when
solving this problem?
3.Which figures in the last group are whatnots? What type of reasoning,
inductive or deductive, do you use when solving this problem?
4.Solve each equation for x. Give a reason for each step in the process.
What type of reasoning, inductive or deductive, do you use when
solving these problems?
a. 4 x 3 8 2 x b. 19 2 x 2
5.A sequence begins 4, 1, 6, 11…
a. Give the next two terms in the sequence. What type of reasoning,
inductive or deductive, do you use when solving this problem?
b. Find a rule that generates the sequence. Then give the 50th term in
the sequence. What type of reasoning, inductive or deductive, do
you use when solving this problem?
Which are whatnots?
For Exercises 710, tell whether each statement is always ,
sometimes , or never true.
7._____ The sum of the measures oftwo acute angles equals the
measure of an obtuse angle.
8._____ If XAY and PAQ are vertical angles, then either X, A, and P
or X, A, and Q are collinear.
9._____ If two angles form a linear pair, then they are complementary.
10._____ If a statement is true, then its converse is true.
m A ____.
m Q is ____.
Presentation On Theme: Lesson 21 Inductive Reasoning In Geometry Presentation Transcript:
1 Lesson 2.1 Inductive Reasoning in GeometryHOMEWORK: Lesson 2.1/1-15 odds,22-24, 31-40, 42EC: Due WednesdayPage 104 Improve Reasoning Skills #1-8
2 Vocabulary Inductive reasoning:make conclusions based on patterns you observeConjecture:conclusion reached by inductive reasoning based on evidenceGeometric Pattern:arrangement of geometric figures that repeat
3 We will be doing this ALOT this year!!Objectives:Use inductive reasoning to find the next term in a number or picture patternTo use inductive reasoning to make conjectures.Mathematicians use Inductive Reasoning to find patterns which will then allow them to conjecture.We will be doing this ALOT this year!!
4 A generalization made with inductive reasoning ConjecturesA generalization made with inductive reasoning EXAMPLES:Bell rings M, T, W, TH at 7:40 amConjecture about Friday?Chemist puts NaCl on flame stick and puts into flame and sees an orange-yellow flame. Repeats for 5 other substances that also contain NaCl also producing the same color flame.Conjecture?
5 reasoning that is based on patterns you observe.Inductive Reasoning reasoning that is based on patterns you observe.Ex. 1: Find the next term in the sequence:A) 3, 6, 12, 24, ___, ___B) 1, 2, 4, 7, 11, 16, 22, ___, ___C) ,___, ___
6 Solutions Ex. 1: Find the next term in the sequence:A) 3, 6, 12, 24, ___, ___B) 1, 2, 4, 7, 11, 16, 22, ___, ___C)4896Rule: x22937Rule: +1, +2, +3, +4, Rule: divide each section by half
30 Solutions
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Reasoning And Proofs Chapter Review
2.1 Conditional Statements
Write the if-then form, the converse, the inverse, the contrapositive. and the biconditional of the conditional statement.
Question 1.Two lines intersect in a Point.Answer:If two lines intersect, then the intersection is a point.Converse:If the intersection of lines is a point, the two lines intersect.Inverse:If two lines do not intersect, then a point is not intersection.Contrapositive:If a point is not intersection, then two lines do not intersect.Biconditional:Two lines intersect if and only if the intersection is a point.
Question 2.4x + 9 = 21 because x = 3.Answer:If x = 3, then 4x + 9 = 21Converse:If 4x + 9 = 21, then x = 3Inverse:If x 3, then 4x + 9 21Contrapositive:If 4x + 9 21, then x 3Biconditional:x = 3 if and only if 4x + 9 = 21Note that x + 3 is hypotesis and 4x + 9 = 21 is conclusion in this sentence.
Question 3.Supplementary angles sum to 180°.Answer:If angles are supplementary, then their sum is 180°.Converse:If the sum of angles is 180°, then these angles are supplementary.Inverse:If angles are not supplementary, then these angles are not supplementary.Biconditional:Angles are supplementary if and only if then their sum is 180°
Question 4.
2.3 Postulates and Diagrams
Use the diagram at the right to determine whether you can assume the statement.
Question 9.Points A, B, C, and E are coplanar.Answer:Points lie on two parallel lines, meaning that they lie in same plane, so ther are coplanar.
Question 16.
Question 5.
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Study Skills: Using The Features Of Your Textbook To Prepare For Quizzes And Tests
Mathematical Practices
Question 1.Provide a counter example for each false conditional statement in Exercises 17 24 on page 71.
Question 2.Create a truth table for each of your answers to Exercise 59 on page 74.Answer:
Question 3.For Exercise 32 on page 88. write a question you would ask your friend about his or her interpretation.Answer:
Performance Task: Induction And The Next Dimension
Mathematical Practices
Explain the purpose of justifying each step in Exercises 5-14 on page 96.Answer:
Create a diagram to model each statement in Exercises 5-10 on page 103.Answer:
Question 3.Explain why you would not be able to prove the statement in Exercise 21 on page 113 if you were provided with the given information or able to use an postulates or theorems.Answer:
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What Type Of Reasoning Inductive Or Deductive Do You Use When Solving This Problem
Inductive reasoning worksheet. Worksheets are lesson inductive reasoning inductive vs deductive wkst inductive reasoning geometry 2 geometry inductive and deductive reasoning inductive reasoning sample test 1 inductive and deductive reasoning 2075 4 7 3dwwhuqvdqgqgxfwlyh5hdvrqlqj 1 1a practice inductive versus deductive reasoning. Displaying all worksheets related to inductive reasoning. Solve each equation for x.
Predict the next number. Deductive reasoning exercises for attention and executive functions real life problem solving carrie b. Describe a pattern in the sequence of numbers.
First they determine if each conjecture is true or false based on the. Sketch the next figure in the pattern. What type of reasoning inductive or deductive do you use when solving this problem.
4x 3 2 x 8 2x b. Showing top 8 worksheets in the category inductive reasoning. Some of the worksheets displayed are lesson inductive reasoning inductive vs deductive wkst inductive reasoning geometry 2 geometry inductive and deductive reasoning inductive reasoning sample test 1 inductive and deductive reasoning 2075 4 7 3dwwhuqvdqgqgxfwlyh5hdvrqlqj 1 1a practice inductive versus deductive reasoning.
Sketch the next figure in the pattern. Patterns and inductive reasoning worksheet. They are given a statement and required to do 3 things.
Showing top 8 worksheets in the category inductive reasoning to make conjectures. Give a reason for each step in the process. Predict the next number.
Lesson 23 Postulates And Diagrams
Monitoring progress
Question 1.Use the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?Answer:
Use the diagram in Example 2 to write an example of the postulate.a. Two Point Postulate
Line Intersection Postulate Answer: If two lines intersect, then their intersection is exactly one point.The intersection of the line p and q is point H.
Question 7.Three Point Postulate Answer:
Plane-Line Postulate Answer:If two points lie in a plane, then the line containing them lies in the plane.Points H and G lie in a plane M, so line p lies in plane M
In Exercises 9 12. sketch a diagram of the description.
Question 9.plane P and line m intersection plane P at a 90° angleAnswer:
Question 10.\ in plane P, \ bisected by point A. and point C not on \Answer:Draw the necessary figures and label them properly. Make sure to put a red line across the bisected lines to indicate that they are congruent.
Question 11.\ intersecting \ at point A. so that XA = VAAnswer:
Question 12.\, \, and \ are all in plane P. and point x is the midpoint of all three segments.Answer:Draw the necessary figures and label them properly. Make sure to put a red line across the bisected lines to indicate that they are congruent.
In Exercises 13 20, use the diagram to determine whether you can assume the statement.
Question 13.Planes Wand X intersect at .
H, F, and D are coplanar. Plane T plane S. Point B bisects \. ABH and HBF are a linear pair.
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Big Ideas Math Geometry Answers Chapter 2 Reasoning And Proofs
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Big Ideas Math Book Geometry Answer Key Chapter 2 Reasoning And Proofs
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Question 13.ABSTRACT REASONINGCan you use the equation for an arithmetic sequence to write an equation for the sequence 3, 9, 27, 81. . . . ? Explain our reasoning.Answer:
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Reasoning And Proofs Cumulative Assessment
Question 1.Use the diagram to write an example of each postulate.a. Two Point Postulate : Through any two points, there exists exactly one line.Answer:Read the different postulates and use the diagram to look for an example for each postulate.Passing through two points, A and F there exists exactly one line which is \
b. Line Intersection Postulate : If two lines intersect, then their intersection is exactly one point.Answer: \ intersects \ at exactly one point which is point C.
c. Three Point Postulate : Through any three noncollinear points, there exists exactly one plane.Answer:Points E, B, C there exists exactly one plane which is plane S.
d. Plane-Line Postulate : If two points lie in a plane, then the line containing them lies in the plane.Answer: Points A and F lies in plane T, therefore \ also lies in the plane T.
e. Plane Intersection Postulate : If two planes intersect, then their intersection is a lineAnswer: Planes S and T at \
Question 2.Enter the reasons in the correct positions to complete the two-column proof.Answer:2. AX = DX according to definition of congruent segments.4. XB = XC according to definition of congruent segments.5. AX + XC = AC according to segment addition postulate.6. DX + XB = DB according to segment addition postulate.7. AC = DX + XB according to substitution property of equality.8. AC = BD according to substitution property of equality.9. \ = \ according to substitution property of equality and definition of congruent segments.
Exercise 25 Proving Statements About Segments And Angles
Vocabulary and Core Concept Check
Question 1.How is a theorem different from a postulate?Answer:A postulate is a rule that is accepted to be true without proof and a theorem is a statement that can be proven by using definitions, postulates, and previously proven theorems.
Question 2.COMPLETE THE SENTENCEIn a two-column proof, each __________ is on the left and each __________ is on the right.Answer: In a two-column proof, each statement is on the left and each reason is on the right.
Monitoring Progress and Modeling with Mathematics
In Exercises 3 and 4. copy and complete the proof.
Question 3.
Answer: Reflexive Property of Angle Congruence
Question 7.If G H. then H G.Answer:
Question 8.\Answer: The statement is talking about reflexity involving line segments, we can say that this observes the Reflexive Property of Segment Congruence
Question 9.If \, then \.Answer:
Question 10.If L M and M N, then L N.Answer: Since the if-then statement is talking about transitivity involving angles, we can say that this observes the Transitive Property of Angle Congruence
PROOFIn Exercises 11 and 12, write a two-column proof for the property.
Question 11.Reflexive Property of Segment Congruence Answer:
Transitive Property of Angle Congruence Answer:
From AB = BC and AB = FG substitution property of equalityBC = FGFrom BC = FG and DF = FG substitution property of equality\ \
Question 19.Explain why you do not use inductive reasoning when writing a proof.Answer:
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Lesson 21 Conditional Statements
Monitoring Progress
Use red to identify the hypothesis and blue to identify the conclusion. Then rewrite the conditional statement in if-then form.
Question 1.All 30° angles are acute angles.Answer: If an angle measures 30°, then it is acute angle.
Question 2.2x + 7 = 1. because x = 3.Answer: If x = -3, then 2x + 7 = 1
In Exercises 3 and 4, write the negation of the statement.
Question 3.Answer: The shirt is not green
Question 4.The Shoes are not red.Answer: The shoes are red
Question 5.Repeat Example 3. Let p be the stars are visible and let q be it is night.Answer:p q If the stars are visbile, then it is night Trueq p If it is night, then the stars are visible Falsep q If the stars are not visbile, then it is not night Falseq p If it is not night, then the stars are not visible True
Use the diagram. Decide whether the statement is true. Explain your answer using the definitions you have learned.
Question 6.JMF and FMG are supplementary.Answer: True. They are a linear pair
Question 7.Point M is the midpoint of \.Answer: False. There is mo marking to show \ \
Question 8.JMF and HMG arc vertical angles.Answer: True. They share a vertex and their sides for, opposite rays.
Question 9.Answer: False. You cannot assume their intersection is a right angle without markings.
Question 14.Make a truth table for the conditional statement p ~ q.Answer:
Vocabulary and Core Concept Check
Question 3.If a polygon is a pentagon, then it has five sides.Answer: