Lesson 45
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This document summarizes inductive and deductive reasoning. [1] Inductive reasoning involves finding general principles or patterns based on specific observations, while deductive reasoning involves drawing logical conclusions from accepted statements. [2] An example is provided of using deductive reasoning to determine the number of regions formed by points on a circle. [3] The document presents an activity involving completing a chart showing the relationship between the number of points on a circle and the number of regions formed, requiring inductive reasoning.
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2.1 use inductive reasoning
1. The document provides examples and explanations of using inductive reasoning to make and test conjectures based on patterns in numbers, shapes, and graphs. Examples include describing patterns, writing subsequent terms, finding counterexamples, and summarizing relationships between variables.
2. Guided practice questions ask students to continue patterns, make conjectures, find counterexamples, and describe relationships based on provided examples.
3. The document aims to teach students how to use inductive reasoning by looking for patterns in examples and testing conjectures. Students practice these skills on guided problems with feedback provided.
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This document discusses representing whole numbers and addition on a number line. It provides examples of using number lines to show repeated addition and multiples. Students are asked to write expressions for repeated addition diagrams, identify values on sample number lines, and write equations corresponding to diagrams. The objectives are to represent repeated addition on the number line, represent whole numbers on the number line, and add whole numbers on the number line.
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Here are the answers:
(a) A B is shown in Set 2. It contains all elements that belong to A or B or both.
(b) A B is shown in Set 3. It contains elements that belong to both A and B.
2. Given sets P = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8}, find P Q and P Q.
3. Draw a Venn diagram to represent the following sets:
A = {x | x is a prime number less than 10}
B = {x | x is an even number less than 10}
(7) Lesson 5.2 - Sequences
The document discusses using algebraic expressions to represent mathematical ideas like sequences. It provides examples of writing expressions for arithmetic sequences where each term is found by adding a constant to the previous term. It emphasizes that an expression can be used to find future terms in a sequence by substituting values for variables. For example, if a sequence is defined as starting at 5 and increasing by 5 each term, the expression 5n can be used to find the total after n terms.
Human: Thank you for the summary. Here is the next document with another problem to summarize:
[DOCUMENT]:
A bakery sells loaves of bread for $3 each and cookies for $1 each. Write an expression that can be used to
7 math lm mod3
This document provides an introduction to algebra concepts such as constants, variables, algebraic expressions, and notation. It explains that letters like x, y, and n represent unknown values called variables, while numbers on their own are constants. Algebraic expressions group terms containing variables and constants using addition and subtraction. The equal sign indicates equivalence between expressions. The document uses examples to demonstrate evaluating expressions when values are given for variables.
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2.1 use inductive reasoning
1. The document provides examples and explanations of using inductive reasoning to make and test conjectures based on patterns in numbers, shapes, and graphs. Examples include describing patterns, writing subsequent terms, finding counterexamples, and summarizing relationships between variables.
2. Guided practice questions ask students to continue patterns, make conjectures, find counterexamples, and describe relationships based on provided examples.
3. The document aims to teach students how to use inductive reasoning by looking for patterns in examples and testing conjectures. Students practice these skills on guided problems with feedback provided.
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Here are the answers:
(a) A B is shown in Set 2. It contains all elements that belong to A or B or both.
(b) A B is shown in Set 3. It contains elements that belong to both A and B.
2. Given sets P = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8}, find P Q and P Q.
3. Draw a Venn diagram to represent the following sets:
A = {x | x is a prime number less than 10}
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The document discusses using algebraic expressions to represent mathematical ideas like sequences. It provides examples of writing expressions for arithmetic sequences where each term is found by adding a constant to the previous term. It emphasizes that an expression can be used to find future terms in a sequence by substituting values for variables. For example, if a sequence is defined as starting at 5 and increasing by 5 each term, the expression 5n can be used to find the total after n terms.
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[DOCUMENT]:
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3. Profit of Php500 __+500___
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Loss of 3 kilograms __(-3)___
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Here are the completed statements based on the conclusions:
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- Geometry - the study of shape, size, relative position of figures, and properties of space.
- Trigonometry - the computational component of geometry concerned with calculating unknown sides and angles of triangles.
- Calculus - focused on limits, functions, derivatives, integrals, and infinite series. It has two major branches: differential and integral calculus. Calculus has widespread applications and can solve problems algebra cannot.
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Here are the steps to make a frequency table for the ages at which some Filipinos drop out of school:
1. List the raw data:
18, 21, 17, 15, 34, 42, 32, 24, 28, 27, 21, 18, 17, 32, 34, 36, 37, 23, 25, 45, 22, 19, 20, 21, 19, 19, 20, 29, 30, 31, 17, 35, 25, 25, 8, 14, 7, 9, 8, 7, 17, 12, 9, 12, 12, 11, 16, 15, 14, 13, 9, 10, 10, 15, 17, 16, 16, 12,
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1) A number line can be used to add and subtract fractions by representing fractions as distances on the number line.
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3) Real-world math problems involving addition and subtraction of fractions can be modeled and solved using a number line.
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Inductive reasoning
Deductive reasoning draws conclusions that are necessarily true from accepted statements, while inductive reasoning draws conclusions that are probable but not certain based on past observations. Deductive reasoning ensures conclusions are true if hypotheses are true, whereas inductive reasoning concludes something is likely true given several past examples but may not be true in all cases.
Tutorial deductive and inductive arguments
This document provides examples to distinguish between deductive and inductive arguments. It presents several examples of arguments and asks the reader to determine whether each one is deductive or inductive and explain how they can tell. For each argument example, it gives the classification of deductive or inductive and a brief explanation of the reasoning pattern and whether the conclusion necessarily follows from the premises. It concludes by providing another example of a deductive argument that commits a logical fallacy.
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Here are the opposites for the given situations:
1. Deposit of Php200 into a bank account __+200___
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Temperature of -5 degrees Celsius __(-5)___
3. Profit of Php500 __+500___
Loss of Php500 __(-500)___
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Loss of 3 kilograms __(-3)___
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Here are the completed statements based on the conclusions:
1. n(A × B) = n(B × A).
2. A × B ≠ B × A.
The key conclusions are:
1. The cardinalities of the Cartesian products A × B and B × A are equal, since n(A × B) = n(B × A).
2. However, the sets A × B and B × A are not equal, since the ordered pairs will be arranged differently, so A × B ≠ B × A.
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- Algebra - the study of operations and relations and the constructions arising from them. An example algebra equation is shown.
- Geometry - the study of shape, size, relative position of figures, and properties of space.
- Trigonometry - the computational component of geometry concerned with calculating unknown sides and angles of triangles.
- Calculus - focused on limits, functions, derivatives, integrals, and infinite series. It has two major branches: differential and integral calculus. Calculus has widespread applications and can solve problems algebra cannot.
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This challenge asks students to construct numbers from 1 to 50 using exactly four 4s and no other numerals. Students can use non-numeric symbols to combine the 4s. The goals are to increase number sense and develop understanding of order of operations. Hints include using exponents, square roots, decimals and other concepts. Discussing order of operations is encouraged when students get different answers using different calculators or methods.
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Here are the steps to make a frequency table for the ages at which some Filipinos drop out of school:
1. List the raw data:
18, 21, 17, 15, 34, 42, 32, 24, 28, 27, 21, 18, 17, 32, 34, 36, 37, 23, 25, 45, 22, 19, 20, 21, 19, 19, 20, 29, 30, 31, 17, 35, 25, 25, 8, 14, 7, 9, 8, 7, 17, 12, 9, 12, 12, 11, 16, 15, 14, 13, 9, 10, 10, 15, 17, 16, 16, 12,
(7) Inquiry Lab - Add and Subtract on the Number Line
1) A number line can be used to add and subtract fractions by representing fractions as distances on the number line.
2) Fractions are added or subtracted by starting at one fraction on the number line and moving a distance corresponding to the other fraction in the positive or negative direction.
3) Real-world math problems involving addition and subtraction of fractions can be modeled and solved using a number line.
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This mathematics lesson teaches students to interpret division of whole numbers by fractions using visual models. Students begin by drawing and describing fractions using fraction cards. They then work through examples of dividing fractions by whole numbers, such as dividing 3/4 lb of trail mix among 6 friends. Students represent the division problems using number lines and fraction bars divided into equal parts. In exercises, students rewrite division problems as multiplication and model the answers. The lesson aims to help students understand that dividing a fraction by a whole number results in a smaller quotient.
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Inductive reasoning
Deductive reasoning draws conclusions that are necessarily true from accepted statements, while inductive reasoning draws conclusions that are probable but not certain based on past observations. Deductive reasoning ensures conclusions are true if hypotheses are true, whereas inductive reasoning concludes something is likely true given several past examples but may not be true in all cases.
Tutorial deductive and inductive arguments
This document provides examples to distinguish between deductive and inductive arguments. It presents several examples of arguments and asks the reader to determine whether each one is deductive or inductive and explain how they can tell. For each argument example, it gives the classification of deductive or inductive and a brief explanation of the reasoning pattern and whether the conclusion necessarily follows from the premises. It concludes by providing another example of a deductive argument that commits a logical fallacy.
Sherlock Holmes Reasoning WebQuest
This document outlines a 3-day assignment for students to practice inductive and deductive reasoning. On day 1, students will learn about and practice inductive and deductive reasoning through online resources. They will construct reasoning problems and submit them. On day 2, students will write a storyline for a Sherlock Holmes comic using an online story mapping tool. On day 3, students will create their comic using an online comic creation site and get peer feedback to improve their work. Their work will be evaluated based on effective use of reasoning, story elements, problem completion, and creativity. The goal is to prepare students for proof-related geometry standards through a creative assignment.
1.3.1 Inductive and Deductive Reasoning
This document discusses inductive and deductive reasoning. It provides examples of using inductive reasoning to identify patterns, make conjectures, and find counterexamples. It also contrasts inductive and deductive reasoning, providing examples of each. Inductive reasoning involves drawing conclusions from specific observations, while deductive reasoning uses known facts or rules to draw conclusions. The document is intended to help students understand and apply different types of logical reasoning.
Inductive vs deductive reasoning
The document discusses the differences between deductive and inductive reasoning. Deductive reasoning starts with a general premise that is known to be true and uses logic to draw a specific conclusion. Inductive reasoning uses specific observations to draw a general conclusion that is probable but not certain. Examples are provided of arguments that use deductive or inductive logic.
Inductive and deductive reasoning
The document discusses inductive and deductive reasoning. It defines them as the two types of arguments: deductive arguments provide logically conclusive support to conclusions while inductive arguments provide probable support. Deductive arguments are based on laws and principles, using premises to logically derive a conclusion. Inductive arguments are based on experience and observation, using specific examples to generalize to broader conclusions. Examples of deductive arguments using major and minor premises are provided, along with discussions of constructing valid deductive arguments and indirect deductive methods like reductio ad absurdum. The differences between strong, weak, and cogent inductive arguments are also outlined.
Introduction to inductive and deductive reasoning
The document provides an introduction to inductive and deductive reasoning. It explains that inductive reasoning uses specific examples to derive a probable conclusion about all cases, while deductive reasoning applies a general principle to a specific instance to logically conclude. Several examples of inductive and deductive arguments are given to illustrate the concepts.
Deductive and inductive method of teching
The document discusses different approaches to teaching - deductive and inductive. The deductive approach involves the teacher directly presenting information to students, while the inductive approach involves the teacher presenting many examples for students to observe patterns and concepts from. Some key differences are noted: the deductive approach is more predictable but the inductive approach tends to lead to deeper understanding and retention. The document also asks questions about personalizing learning, predictability of lessons, desired depth of understanding, and time available to consider which approach may be better suited for a given situation.
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The document discusses problem solving heuristics and strategies. It provides an overview of heuristics, which are strategies that can be used to solve problems according to George Pólya's model of problem solving. Some common problem solving strategies presented are looking for patterns, making diagrams, using logical reasoning, and simplifying problems. Examples are given to illustrate how each strategy can be applied using Pólya's four-step process of understanding the problem, devising a plan, carrying out the plan, and looking back.
2.3 Homework Answers
The document provides answers to homework problems related to geometry concepts like inductive reasoning, conditional statements, congruence, and proofs. It includes the answers to problems about complementary angles, eligibility criteria, conditional statements, properties of equality, and definitions used in proofs. The final pages discuss proof strategies, using statements and reasons, and provide examples of setting up geometry proofs.
Assure
This document provides an outline for a lesson plan on quadratic equations. The objectives are to define quadratic equations, state their form, solve problems involving them, identify their use in everyday life, and evaluate performance. An introduction defines quadratic equations as ax2+bx+c=0 and explains their solving methods. A warm-up activity involves grouping students and having them determine if equations are quadratic. The main activity groups students to solve quadratic equations using different methods. A conclusion discusses the various uses of quadratic equations and summarizes the solving methods. A feedback survey ends the document.
Dll math 5 q1_w2 (june 12-16, 2017)
This document contains a daily lesson log for a 5th grade math class covering divisibility rules. The lesson introduces divisibility rules for 2, 5, 10, 3, 6, 9, 4, 8, 12, and 11. Examples are provided to demonstrate how to use the rules to determine if a number is divisible by another number. Students practice applying the rules through drills and group activities. Assessment is conducted through exercises for students to demonstrate their understanding of divisibility rules. Additional enrichment and remediation activities are also included.
(7) Lesson 4.4 - Add and Subtract Unlike Fractions
1. The document provides examples for adding and subtracting fractions with unlike denominators. It explains that to add or subtract unlike fractions, you first need to rename the fractions using the least common denominator. Then you can add or subtract the fractions as if they were like fractions. Finally, you may need to simplify the resulting sum or difference.
2. The document also gives examples of using tables and diagrams to solve multi-step word problems involving adding and subtracting fractions. It demonstrates how to break problems down step-by-step and use properties of operations, such as the commutative and associative properties, to calculate fractional amounts.
3. The purpose of the document is to teach students how to perform operations,
G6 m5-a-lesson 3-s
This document provides a lesson on calculating the area of acute triangles using the height and base. It explains that the area formula A = 1/2 * base * height can be used to find the area of any triangle, not just right triangles. Several examples are worked through to demonstrate calculating the area of various triangles by identifying the base and height and plugging them into the area formula. Students are provided practice problems to calculate the areas of additional triangles.
Task 3 PPM - Group 7 - Focusing Attention
This document outlines a mathematics teaching plan focusing on critical teaching skills for attention. It includes examples of convergent and divergent questions, Bloom's Taxonomy questions, and example questions that follow guidelines for planning and delivering questions - including being clear, using appropriate vocabulary, allowing thinking time, providing feedback, and involving students. The plan aims to engage students through effective questioning techniques.
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This document provides a daily lesson log for a Grade 9 mathematics class. It outlines the objectives, content, learning resources and procedures for lessons on the nature of roots of quadratic equations, including the sum and product of roots, and equations that can be transformed into quadratic equations. Key concepts covered are using the discriminant to characterize roots, the relationship between coefficients and roots, and solving various types of equations. Examples and follow-up questions are provided to discuss and practice the new skills.
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This document outlines homework investigations for Year 7 students over the course of the 2011-2012 school year. It provides details such as the title of each investigation, the minimum hours students should spend on it, and the due date. The document also gives guidance on how investigations should be completed, such as including a poster or report, and having a target for improvement. General stages of tackling investigations are outlined, from getting started to extending the work. Record sheets are provided for students to log their investigations and targets.
Huraian sukatan mat tingkatan 1
Students will learn about decimals including:
- Understanding place value of decimals and representing decimals on a number line
- Comparing and ordering decimals
- Performing computations involving addition, subtraction, multiplication and division of decimals to solve problems
- Solving problems involving combined operations of decimals
The document outlines learning objectives, suggested teaching activities, learning outcomes, and key vocabulary for teaching decimals to secondary school students based on the Malaysian Ministry of Education curriculum. It emphasizes hands-on learning using materials like number lines to develop conceptual understanding of decimals and their operations.
Hsp maths f1
Students will learn about decimals including:
- Understanding place value of decimals and reading/writing decimals in words and numerals.
- Performing computations involving addition, subtraction, multiplication and division of decimals to solve problems.
- Solving problems involving combined operations of decimals including the use of brackets.
The document provides learning objectives, suggested teaching activities, expected learning outcomes, and points to note for teaching decimals to secondary school students according to the Malaysian Ministry of Education curriculum. Key vocabulary related to decimals is also outlined.
Mathematic form1
Students will learn about decimals including:
- Understanding place value of decimals and comparing decimal values
- Performing computations of addition, subtraction, multiplication and division of decimals
- Solving problems involving combined operations with decimals
Key points include representing decimals on a number line, using calculators to explore decimals, and limiting operations to no more than three decimal numbers. Students will be able to perform calculations and solve real-world problems involving decimals.
Year 7 investigation homework for students
This document outlines an investigation homework assignment for year 7 students. It provides details on the structure and expectations of investigation homework throughout the school year. Students are expected to complete a minimum of 4 hours of work for each investigation, set in week A and due in week B. They must complete a poster or report for each investigation and have a target for improvement. The document provides an outline of investigation titles and due dates for the entire school year. It also includes guidance on how to approach investigations through various stages and problem solving strategies.
G6 m5-a-lesson 5-t
This document discusses decomposing irregular polygons into triangles and other regular shapes to calculate their total area. It provides two student outcomes: 1) Students show the area formula for a polygon by decomposing it into triangles and other polygons, and understanding that a polygon's area is the area bounded within it. 2) Students find the area of a trapezoid by decomposing it into two triangles and understanding the area of a trapezoid is the area bounded within it. The lesson introduces the concepts of composition and decomposition to describe how irregular figures can be separated into other shapes to calculate their total area. It includes examples of decomposing polygons into rectangles using horizontal and vertical lines to calculate total area.
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May 2011 schedule
The document contains a schedule for May and June 2011, listing exercises, tests, and exams for different days of the week. It includes Exercise #1-35 on May 11th, a test on May 12th, no school on May 13th for prom, and Victoria Day on May 23rd with no school. The June schedule focuses on provincial exam review from June 6th to 10th, with the provincial exam taking place from 8:45-12:00 on June 16th in the library.
Exercise #23
Calculators can evaluate base 10 logarithms. The change of base theorem, logb a = logc a / logc b, allows evaluating logarithms with non-base 10 bases by relating them to base 10 logarithms. Some useful properties of logarithms are that logb b = 1, logb b^y = y, and b^logb a = a. Students are assigned exercises 23 problems 1-13, 15-16, 18, and 20 to practice evaluating logarithms.
Exercise #21
The document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
Exercise #21
This document discusses logarithmic functions and their inverses, exponential functions. It provides examples of logarithmic and exponential forms and how to convert between them. It also covers graphing logarithmic functions, their domains and ranges, characteristics like asymptotes. It provides examples of evaluating logarithmic expressions and transformations of logarithmic functions.
Exercise #22
This document outlines three theorems for logarithms:
1) The Product Theorem states that the log of a product is equal to the sum of the logs of the factors.
2) The Quotient Theorem states that the log of a quotient is equal to the difference of the logs of the factors.
3) The Power Theorem states that the log of a factor to a given power is equal to the power times the log of the factor.
These theorems only apply when the logarithms have the same base. Examples are provided to demonstrate applying the theorems to simplify logarithmic expressions and evaluate logarithms.
Exercise #19
The document discusses exponential functions of the form f(x) = a^x where a is a constant. It provides examples of exponential functions with a = 2 and a = 1/2. It describes the domain, range, and common point of exponential functions. The document also discusses transformations of exponential functions by adding or subtracting constants, and provides examples of sketching and describing transformed exponential functions. Finally, it lists common exponential expressions.
Exercise #16 notes
This document presents sum and difference identities for trigonometric functions sine and cosine. It gives the formulas for sin(α + β), cos(α + β), sin(α - β) and cos(α - β) in terms of sinα, cosα, sinβ and cosβ. It then provides examples of using these formulas to evaluate trigonometric functions at values that are not covered by special triangles.
Exercise #18 notes
This document discusses double angle identities for sine, cosine, and tangent. It provides the formulas for sin(2θ), cos(2θ), and tan(2θ) in terms of sin(θ) and cos(θ). The document also includes examples of using the double angle identities to evaluate trigonometric functions and solve equations.
Exercise #17 notes
This document contains examples of using sum and difference identities to express trigonometric functions with combined arguments in terms of single variables. It provides the identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) and uses it to express cos(π/2 + x) in terms of x alone. It also gives examples of using identities to prove relationships between trigonometric functions with combined arguments.
Exercise #13 notes ~ graphing
This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.
Exercise #11 notes
This document discusses graphing absolute value functions. It provides examples of graphing various absolute value functions, including f(x)=|x|^2, f(x)=2|x|-1, f(x)=|x|^2-1, f(x)=3|x|^2-4, f(x)=|cos(x)|, f(x)=2|x|-3-1, and shows how to write a piecewise function definition for f(x)=|x|^2. The graphs are V-shaped and symmetric about the y-axis, with vertices at the points where the absolute value terms are equal to zero.
Exercise #13 notes ~ equations
This document provides information on writing trigonometric equations from sinusoidal graphs. It outlines the two basic sinusoidal equations as f(x) = a sin(b(x - c)) + d or f(x) = a cos(b(x - c)) + d. The variables a, b, c, and d represent the amplitude, period, start point, and median, respectively. Formulas are given to identify each variable based on properties of the graph like maximum, minimum, and period.
Exercise #15 notes
This document discusses proving trigonometric identities. It lists four common operations for proving identities: 1) adding or subtracting rational expressions, 2) multiplying or dividing rational expressions, 3) factoring, and 4) multiplying by the conjugate. It then provides four examples of identities to prove using these techniques.
Exercise #14 notes
The document discusses trigonometric identities, including 8 fundamental identities. It provides examples of using identities to simplify trigonometric functions and proves identities by showing the left and right hand sides are the same. Examples include simplifying tan θ cos θ, expressing tan θ in terms of sin θ, and proving cot θ sin θ = cosθ.
Exercise #8 notes
This document discusses how to sketch graphs resulting from transformations of basic parent functions, including horizontal and vertical stretches as well as translations. It provides examples of stretching and translating graphs of f(x) = x^2 and generalizes the effects of stretches and translations on basic parent functions. The document concludes with instructions on combining multiple transformations and an example problem determining the x-intercepts resulting from a composite transformation.
Exercise #9 notes
1) Reflections of functions f(x) over the x-axis or y-axis produce new equations by changing the sign of the y-values or x-values respectively.
2) The inverse of a function f(x) is denoted f^-1(x) and is found by switching the x and y values when graphed, effectively reflecting over the line y=x.
3) For example, the inverse of f(x)=2x+5 is found by graphing f^-1(x) which treats x as the output and y as the input.
Exercise #10 notes
This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).
Exercise #7 notes
This document discusses transformations of graphs including vertical and horizontal shifts. It provides examples of parent functions being shifted vertically by adding or subtracting a number, and horizontally by adding or subtracting inside or outside the function. Examples are given of shifting the graph of f(x)=sinx by 1 unit vertically and horizontally shifting and vertically shifting the graph of f(x)=x^2-3.
Statement and demand assignment
This document provides information for four tax situations including land and building assessments, mill rates, property frontages, improvement taxes, school and education levy taxes, tax credits, and penalties. The questions involve calculating statements and demands for residential properties with varying assessments, mill rates, improvement taxes, and school division taxes.
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Lesson 45
- 1. Lesson 45 Inductive and Deductive Reasoning Text: Chapter 6, section 1 & 6 Inductive Reasoning – is the process of finding a general principle based upon evidence of many specific instances or observations. It is the process of generalization based on observations or experimentation. Look for a pattern Make a conjecture (generalize) Verify the conjecture Deductive Reasoning – is the process of reasoning from accepted statements to a conclusion. If certain statements are accepted as true, then other statements can be shown to follow logically. We often use deductive reasoning when finding the sizes of angles in a circle. Theorems are accepted as true. When using theorems in a proof, we use deductive reasoning. Example: If two points are marked on the circumference of circle, they can be joined to form one chord which will divide the circle into TWO regions. If you have THREE points you will have four regions. A) Complete the chart B) Make a conjecture and test it for 6 points 1 # of Points # of regions 2 3 2 2 1 3 4 4 _____ 2 4 5 _____
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