Perry High School. Geometry: Week 5

Transcription

1 Geometry: Week 5 Monday: Exam 1a Debrief Tuesday: Exam 1b Wednesday: 2.1 Conditional Statements Thursday: 2.2 Definitions and Biconditional Statements Friday: 2.2 Work Day Next Week 2.3, 2.4, 2.5 1

2 Monday: Mindfulness Training This week: working with difficulty king_with_difficulties.mp3 2

3 Debrief Exam 1a Review definitions Work page 64, Chapter Standardized Test 3

4 Tuesday: Mindfulness Training STOP Meditation 4

5 Exam 1b Day. 5

6 Wednesday: Mindfulness Training This week: working with difficulty king_with_difficulties.mp3 6

7 Reasoning and Proof Basis of reliable knowledge Starting Chapter 2 Foundation of computer programming 2.1: Conditionals 1 DAY! Homework: Due when class starts Tomorrow Guided Practice: p., 75, 1-8 Practice and Applications p., 75, odd 51, 55, 56, 64, 68, 74 7

8 Statements Statements a.k.a. a claim a sentence that is either true or false, but not both. 8

9 Statements a.k.a. a claim a sentence that is either true or false, but not both. Statements The following are statements It is raining. The moon is made of cheese. Five plus three is eight. 9

10 Statements a.k.a. a claim a sentence that is either true or false, but not both. Statements The following are statements It is raining. The moon is made of cheese. Five plus three is eight. Not statements Dag nabbit! 5 o clock 10

11 Parts of Conditionals Conditional Statements have two parts: 1. Hypothesis gives some condition Usually represented by an IF 2. Conclusion -- tells us what happens Usually represented by a THEN Example: If we meditate, then we grow brain tissue. Hypothesis: We meditate Conclusion: We grow brain tissue 11

12 Working with Conditionals Identify the hypothesis and the conclusion 1. If you want good service, then you take your car to Joe s AAA. 2. If you like tennis, then you play on the tennis team. Rewrite as if-then conditional 3. Today is Monday if yesterday was Sunday. 4. A number is divisible by 4 if it is divisible by 8. 12

13 Counterexample, redux Counterexample an example that shows something is false. To show a statement is false, you use a counterexample. Find counterexamples 1. If x 2 =16, then x=8. 2. A point may lie on at most two lines. 3. Dr. Bond does not wear glasses. 13

14 Converse Converse the converse of a statement is formed by switching the hypothesis and conclusion. 14

15 Converse Converse the converse of a statement is formed by switching the hypothesis and conclusion. Statement: If you don t blink, then you will be okay. Converse: If you are okay, then you don t blink. 15

16 Converse the converse of a statement is formed by switching the hypothesis and conclusion. Converse Statement: If it rains, then the grass is wet. Converse: If the grass is wet, then it rained. Statement: If I am quick, I should play basketball. Converse:??? 16

17 Converse the converse of a statement is formed by switching the hypothesis and conclusion. Converse Statement: If it rains, then the grass is wet. Converse: If the grass is wet, then it rained. Statement: If I am quick, I should play basketball. Converse: If I play basketball, then I am quick. 17

18 Negation Negation the negative of a statement 18

19 Negation the negative of a statement Negation Statement: I am tall Negation: I am not tall 19

20 Negation the negative of a statement Negation Statement: I am tall Negation: I am not tall Statement: Fish can swim. Negation:??? 20

21 Negation the negative of a statement Negation Statement: I am tall Negation: I am not tall Statement: Fish can swim. Negation: Fish can not swim. 21

22 Inverse Inverse-when you negate the hypothesis and conclusion of a conditional statement. 22

23 Inverse-when you negate the hypothesis and conclusion of a conditional statement. Inverse Statement: If it rains, then the grass is wet. Inverse: If it does not rain, then the grass is not wet. 23

24 Contrapositive Contrapositive the inverse of the converse of a conditional statement; when you negate the hypothesis and conclusion of the converse of a conditional statement. 24

25 Contrapositive Contrapositive the inverse of the converse of a conditional statement; when you negate the hypothesis and conclusion of the converse of a conditional statement. Statement: If it rains, the grass is wet. Converse: Contrapositive: 25

26 Contrapositive Contrapositive the inverse of the converse of a conditional statement; when you negate the hypothesis and conclusion of the converse of a conditional statement. Statement: If it rains, the grass is wet. Converse: If the grass is wet, then it rains. Contropositive: If the grass is not wet, then it did not rain. 26

27 Equivalent Statements Equivalent has the same truth value. Original statements and their contropositives are equivalent. Inverse and converse statements are equivalent. 27

28 Recall: Postulates Ruler Addition Postulate Segment Addition Postulate Protractor Postulate Angle Addition Postulate 28

29 2.1 Postulates, p. 73 Postulate 5: Through any two points there exists exactly one line. Postulate 6: A line contains at least two points. Postulate 7: If two distinct lines intersect, then their intersection is exactly one point. Postulate 8: Through any three noncollinear points there exists exactly one plane. 29

30 2.1 More Postulates, p. 73 Postulate 9: A plane contains at least three noncollinear points. Postulate 10: If two points lie on a plane, then the line containing them lies in the plane. Postulate 11: If two planes intersect, then their intersection is a line. 30

31 2.1 Work Due when class starts Tomorrow Guided Practice Page 75, 1-8 all Practice and Applications Page odd (check your work!) 51, 55, 56, 64, 68, 74 Show Instructor When Finished 31

32 Thursday: Mindfulness Training This week: working with difficulty king_with_difficulties.mp3 32

33 Debrief 2.1 Questions on Practice and Applications? Spot Check While Reading 2.2 Mixed Review p. 78: Evens 33

34 2.2 Definitions / Biconditionals Note: 2 Days Checking work on Day 2 Day One Lecture Guided Practice HW -- Mixed Review 34

35 Use definitions to justify claims. Goals More generally, this is part of using foundational knowledge to justify how you know things. 35

36 Perpendicular Lines Two lines are perpendicular if they intersect to form a right angle. Perpendicular 36

37 Line Perpendicular to Plane A line is perpendicular to a plane if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it. 37

38 only-if is a pseudoform of a conditional statement, it s a conditional but backwards. Only-If It rains only if the grass is wet. Warning: Looks like it should be if the grass is wet, then it rained. NO! It turns into, If it rains, then the grass is wet. 38

39 Only-If Only if I go to the movies then I ll meet you. Translate:??? I ate too much pie only if my stomach hurts. Translate:??? 39

40 Only-If Only if I go to the movies then I ll meet you. Translate: If I meet you, then I go to the movies. I ate too much pie only if my stomach hurts. Translate: If I ate too much pie, then my stomach hurts. 40

41 Biconditional Statements If and only if aka iff A two direction conditional statement A conditional statement and it s converse joined together 41

42 Biconditional Statements If and only if aka iff A two direction conditional statement A conditional statement and it s converse joined together Two segments are congruent if and only if they have the same measure. You may go to the movies Friday night if and only if you clean your room. 42

43 2.2, Day 1 Guided Practice Page 82, 1-12 Page 85, By end of class on day 2 Page all 46, Show Instructor When Completed 43

44 Friday: Mindfulness Training This week: working with difficulty king_with_difficulties.mp3 44

45 2.2 Work Day Page all 46, Show Instructor When Completed Next Week: 2.3, 2.4,