Inductive Reasoning and Conditional Statements Chapter 2-1 Mr. Dorn.

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Presentation transcript:

Inductive Reasoning and Conditional Statements Chapter 2-1 Mr. Dorn

2-1 Inductive Reasoning Inductive reasoning: Conjecture: Educated guessing based on gathered data and observations. Example 1: When a door is open, the angle the door makes with the door frame is complementary to the angle the door makes with the wall. Write a conjecture about the relationship of the measures of the two angles. The measures of the two angles add up to 90 degrees. Conclusion!

2-1 Inductive Reasoning Example 2: For points A, B, C, and D, AB = 5, BC = 10, CD = 8, and AD = 12. Make a conjecture and draw a figure to illustrate your conjecture. Given: Points A, B, C, and D, AB = 5, BC = 10, CD = 8 and AD = 12. Conjecture: The points form a four-sided figure! A BC D

2-1 Inductive Reasoning Counterexample: One example that disproves a conjecture! Example 3: Given that the points A, B, and C are collinear and B is between A and C, Juanita made a conjecture that B is the midpoint of. Determine if her conjecture is true or false. Explain your answer. False. ABC

2-2 Conditional Statements Conditional Statements: If-then statements with a hypothesis and conclusion. Hypothesis follows the “If” Conclusion follows the “then”. If two angles are adjacent, then they share a common ray. hypothesisconclusion

2-2 Conditional Statements Converse of a Statement: If-then statement formed by exchanging the hypothesis and conclusion. If two angles are adjacent, then they share a common ray. hypothesisconclusion If two angles share a common ray, then they are adjacent. Converse: hypothesisconclusion

2-2 Conditional Statements Inverse of a Statement: If-then statement formed by negating the hypothesis and conclusion. If two angles are adjacent, then they share a common ray. hypothesisconclusion If two angles are not adjacent, then they do not share a common ray. Inverse:

2-2 Conditional Statements Contrapositive of a Statement: If-then statement formed by exchanging and negating the hypothesis and conclusion. If two angles are adjacent, then they share a common ray. hypothesisconclusion If two angles do not share a common ray, then they are not adjacent. Contrapositive: hypothesisconclusion