inductive reasoning and conditional statements chapter 2-1 mr. dorn
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.
AC
False.
A B C
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.
hypothesis conclusion
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.
hypothesis conclusion
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.
hypothesis conclusion
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.
hypothesis conclusion
If two angles do not share a common ray, then they are not adjacent.
Contrapositive:
hypothesisconclusion