1-4 Inductive reasoning Homework: 4-6, 10-14, 19-22

In this Chapter I can… 1-1: Use correct notation and add segments and angles 1-2: Use a compass to draw basic constructions 1-3: Calculate distances and midpoints 1-4: Use inductive reasoning identify patterns, make predictions, and create counterexamples 1-5: Write if-then conditional statements 1-6: Use deductive reasoning to draw conclusions from conditional statements 1-7: Write a proof

5 6 1 8 3 2 7 4 Draw a circle! Draw a point anywhere on the circle. Count how many regions are in the circle. Draw another point anywhere on the circle. Draw a line to connect all the dots with each other. Repeat steps 2-4. 6 1 8 3 2 7 How many regions will there be with 6 dots? How does the number of regions change when you add points? 4

vocabulary Inductive Reasoning: a type of reasoning that reaches conclusions based on a pattern of specific example or past events

Examples Find the next 2 terms 3, 5, 9, 15, 23… 2, 3, 5, 9, 17… 33, 45 33, 65

examples 𝑛 2 +𝑛 𝑛(𝑛+1) Term 1 2 3 4 𝑛 2 +𝑛−1 Term 1 2 3 4

Vocabulary Conjecture: a rule that is based on inductive reasoning Counterexample: an example that shows a conjecture is false

Example Conjecture – A polygon with diagonals has 2 fewer diagonals than sides. Can you find a counterexample?