Miss C's Weekly Forecast Monday Tuesday Wednesday Thursday Friday Quiz 1.3 Unit 1 Review Unit 2 Preassessment Unit 1 Self Evaluation Unit 1 TEST Lesson 8 Continued Lesson7&8 Quiz Lesson 9 Break Break Break Break Break Lesson 7 Unit 2 Intro Student Led Lesson 8 Conferences Reminders: Monday, Jan. 26th - Kahoot! Project due Wednesday, Jan. 28th - Constructions Calculator Project due Wednesday, Jan. 28th - Unit 1 TEST Wed./Thurs. Jan. 28th/29th - Notebooks collected for grading
How do you play Hashiwokakero? GOAL: Connect all of the islands (the circled numbers 1 through 8) with bridges so that any island can eventually be reached from any of the other islands. RULES: The bridges must begin and end at islands Bridges are straight lines that run horizontally or vertically Bridges may not cross other bridges or islands No more than two bridges can connect a pair of islands The total number of bridges connected to each island must match the number on that island
What does this have to do with Geometry? Geometry is all about deductive reasoning. Geometry is like a puzzle!
Lesson 7 Inductive & Deductive Reasoning
Inductive Reasoning *Reasoning based on patterns you observe. *Commonly used in science (scientific method) *You could be wrong! There might be a counterexample that you didn't think of. *Example: We used this reasoning to figure out Hashiwokakero Deductive Reasoning *Reasoning using only facts that are known to be true *You are ALWAYS right! *Example: We used this reasoning to figure out Hashiwokakero
What type or reasoning did we use when we were trying to figure out the rules for Hashiwokakero? Inductive - We drew conclusions about the rules based on what we thought, but we were not always right. What type of reasoning to did we use when we were solving the Hashiwokakero puzzles? Deductive - We only draw bridges when we KNOW where they go.
What type or reasoning did we use when we were trying to figure out the rules for Hashiwokakero? Inductive - We drew conclusions about the rules based on what we thought, but we were not always right. What type of reasoning to did we use when we were solving the Hashiwokakero puzzles? Deductive - We only draw bridges when we KNOW where they go.
Inductive Reasoning *Reasoning based on patterns you observe. *Commonly used in science (scientific method) *You could be wrong! There might be a counterexample that you didn't think of. *Example: We used this reasoning to figure out Hashiwokakero the rules of Deductive Reasoning *Reasoning using only facts that are known to be true *You are ALWAYS right! *Example: We used this reasoning to figure out how to solve Hashiwokakero
Lesson 8 Conditional Statements *TIP: Use red and blue pen in this lesson to help you identify the hypothesis and conclusion*
Conditional Statements 8 Conditional Statement *An if-then statement *Statement p is the hypothesis. *Statement q is the conclusion. * WORD FORM: (1) (2) If p, then q. p implies q. * SYMBOL FORM: p q V Converse *A statement obtained by interchanging the hypothesis and the conclusion. * WORD FORM: If q, then p. * SYMBOL FORM: q p V
EXAMPLES: Identify the hypothesis (p), and the conclusion (q). 1. 2x-1 = 5 implies x=3. 2. If two lines intersect, then they meet at a unique point. 3. If m Y=178, then Y is an obtuse angle.
A conditional statement or its converse can be FALSE!
Counterexample *An example used to prove that a statement is false. *For a counterexample, find an example where the hypothesis is TRUE but the conclusion FALSE. *It only takes ONE counter example to disprove a statement.
Identify the conditional statements & their converses. Write them down Video.mp4
Do these mean the same thing? 1) I say what I mean. I mean what I say. 2) I see what I eat. I eat what I see. 3) I like what I get. I get what I like. 4) I breathe when I sleep. I sleep when I breathe.
PRACTICE
DIRECTIONS: 1) Underline the hypothesis and the conclusion 2) Write the converse. 3) Determine if each statement is true or false. 4) If false, provide a counterexample. Counterexample: TRUE hypothesis FALSE conclusion EXAMPLE #1 True Conditional: If there is a fire, then take the stairs. False T Converse: If you take the stairs, then there is a fire. T counterexample: you take the stairs, but there is not a fire T F
DIRECTIONS: 1) Underline the hypothesis and the conclusion 2) Write the converse. 3) Determine if each statement is true or false. 4) If false, provide a counterexample. Counterexample: TRUE hypothesis FALSE conclusion EXAMPLE #2 True Conditional: False If the power goes off, then the lamp stops working. Converse: If the lamp stops working, the power goes off. counterexample: the lamp stops working, but the power is on (the bulb burned out) F T T T
DIRECTIONS: 1) Underline the hypothesis and the conclusion 2) Write the converse. 3) Determine if each statement is true or false. 4) If false, provide a counterexample. Counterexample: TRUE hypothesis FALSE conclusion EXAMPLE #3 False Conditional: True T ab=0 implies a=0. counterexample: b = 0 Converse: a = 0 implies ab=0 T T F
Biconditional *A combination of a true conditional and its true converse using the words "if and only if" (combines p q and q p ) V V *Every definition can be written as a biconditional * WORD FORM: "if and only if" * SYMBOL FORM: p q V V
Definition: Congruent segments are segments that have equal length. Conditional: If segments are congruent, then they have equal lengths. Converse: If segments have equal lengths, then they are congruent. Biconditional: Segments are congruent if and only if they have equal lengths.
Write the biconditional as two conditionals that are converses of each other. A ray divides an angle into two congruent adjacent angles if and only if it is an angle bisector. 1. If a ray divides an angle into two congruent adjacent angles, then it is an angle bisector. 2. If a ray is an angle bisector, then the ray divides an angle into two congruent adjacent angles.
HOMEWORK: * Complete Lesson 7 & 8 NOTES -See class website for definitions - Equivalent Statements will be done tomorrow in class * Lesson 8 PRACTICE 1 * Make sure your Unit 1 Notes are complete! Will be collected and graded tomorrow!