2-1 Inductive Reasoning & Conjecture INDUCTIVE REASONING is reasoning that uses a number of specific examples to arrive at a conclusion When you assume an observed pattern will continue, you are using INDUCTIVE REASONING. 1

2-1 Inductive Reasoning & Conjecture A CONCLUSION reached using INDUCTIVE REASONING is called a CONJECTURE. 2

2-1 Inductive Reasoning & Conjecture Example 1 Write a conjecture that describes the pattern in each sequence. Use your conjecture to find the next term in the sequence. 3

2-1 Inductive Reasoning & Conjecture Example 1a What is the next term? 3, 6, 12, 24, Conjecture: Multiply each term by 2 to get the next term. The next term is 24 2 = 4 48.

2-1 Inductive Reasoning & Conjecture Example 1b What is the next term? 2, 4, 12, 48, 240 Conjecture: To get a new term, multiply the previous number by the position of the new number. The next term is =1440.

2-1 Inductive Reasoning & Conjecture Example 1c Conjecture: The number of small triangles is the perfect squares. 6 ? 149 What is the next shape?

2-1 Inductive Reasoning & Conjecture The next big triangle should have _____ little triangles

2-1 Inductive Reasoning & Conjecture EX 2 Make a conjecture about each value or geometric relationship. List or draw some examples that support your conjecture. 8

2-1 Inductive Reasoning & Conjecture EX 2a The sum of an odd number and an even number is __________. Conjecture: The sum of an odd number and an even number is ______________. 9 an odd number Example: 1 +4 = 5 Example: = 73

2-1 Inductive Reasoning & Conjecture EX 2b For points L, M, & N, LM = 20, MN = 6, AND LN = L M N

2-1 Inductive Reasoning & Conjecture Conjecture: N is between L and M. OR L, M, and N are collinear. 11 L M N

2-1 Inductive Reasoning & Conjecture Assignment: p.93 – 96 (#14 – 30 evens, 40 – 44, 64 – 66 all) 12

2-3 Conditional Statements CONDITIONAL STATEMENT A statement that can be written in if-then form An example of a conditional statement: IF Portage wins the game tonight, THEN we’ll be sectional champs. 13

2-3 Conditional Statements HYPOTHESIS the part of a conditional statement immediately following the word IF CONCLUSION the part of a conditional statement immediately following the word THEN 14

2-3 Conditional Statements Example 1 Identify the hypothesis and conclusion of the conditional statement. a.) If a polygon has 6 sides, then it is a hexagon. Hypothesis: a polygon has 6 sides Conclusion: it is a hexagon 15

2-3 Conditional Statements Example 1 (continued) b.) Joe will advance to the next round if he completes the maze in his computer game. Hypothesis: Joe completes the maze in his computer game Conclusion: he will advance to the next round 16

2-3 Conditional Statements 17 Example 2 Write the statement in if-then form, Then identify the hypothesis and conclusion of each conditional statement.

2-3 Conditional Statements a.) A dog is Mrs. Lochmondy’s favorite animal. If-then form: If it is a dog, then it is Mrs. Lochmondy’s favorite animal. Hypothesis: it is a dog Conclusion: it is Mrs. Lochmondy’s favorite animal 18

2-3 Conditional Statements b.) A 5-sided polygon is a pentagon. If-then form: If it is a 5-sided polygon then it is a pentagon. Hypothesis: it is a 5-sided polygon Conclusion: it is a polygon 19

2-3 Conditional Statements CONVERSE: The statement formed by exchanging the hypothesis and conclusion 20

2-3 Conditional Statements Example 3 Write the conditional and converse of the statement. Bats are mammals that can fly. Conditional: If it is bat, then it is a mammal that can fly. Converse: If it is a mammal that can fly, then it is a bat. 21

2-3 Conditional Statements Assignment: p (#18 – 30, evens50, 52) 22

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