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4.4: Analyze Conditional Statements

4.4: Analyze Conditional Statements. Vocabulary: a_______________________ is a logical statement that has two parts, a hypothesis and a conclusion. When it is written in an “ if-then form ”, the “if” part is the _______________ and the “then” part is the _____________

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4.4: Analyze Conditional Statements

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  1. 4.4: • Analyze Conditional Statements

  2. Vocabulary: • a_______________________ is a logical statement that has two parts, a hypothesis and a conclusion. When it is written in an “if-then form”, the “if” part is the _______________ and the “then” part is the _____________ • Example: circle the whether or not the underline phrase is the hypothesis or conclusion. • If I water my flowers, then they will grow • (hypothesis/conclusion) (hypothesis/conclusion) • You try: • If I study for my test, then I will do better on my test. • (hypothesis/conclusion) (hypothesis/conclusion) • __________________:when you switch the hypothesis and the conclusion • __________________: when you negate (say opposite of) the hypothesis and conclusion. • _________________: when you switch the hypothesis and conclusion AND negate them.

  3. Rewrite the statement in if-then format. 1. All sharks have a boneless skeleton. 2. When n = 6, n² = 36.

  4. If it is a shark, then it has a boneless skeleton . • If n = 6, then n² = 36.

  5. Write If-then form, converse, inverse, and contrapositive, and determine if each is true or false. Basketball players are athletes. If-then: Converse: Inverse: Contrapositive:

  6. If-then: If they are basketball players, then they are athletes. • Converse: If they are athletes, then they are basketball players. • Inverse: If they are NOT basketball players, then they are NOT athletes. • Contrapositive: If they are NOT athletes, then they are NOT basketball players. True or False?

  7. Vocabulary: • If 2 lines intersect to form right angles, they are _______________ lines • When a statement and its converse are BOTH true, you can write them as a __________________________ statement. This statement contains “_____________”

  8. Write a BICONDITIONAL • If a polygon is equilateral, then all of its sides are congruent. • Converse: • Biconditional:

  9. Converse: If all of the sides are congruent, then it is an equilateral polygon • BICONDITIONAL: A polygon is equilateral if and only if all of its sides are congruent.

  10. 4.4: Apply Deductive Reasoning (note: different than logic in 4.2: Inductive Reasoning) • Vocabulary: • ____________________ reasoning uses facts, definitions, accepted properties, and logic to form logical argument. • ___________________________ if the hypothesis is true, then the conclusion is true • If p, then q • P, therefore q • ___________________________ • If p, then q • If q, then r • P, therefore r

  11. Law of Detachment: • Example: • If you order desert, then you will get ice cream • Sarah ordered desert • Sarah got ice cream

  12. Example: • If you run every day, then you will be in good shape. • Ms. Towner runs every day • Ms. Towner is in good shape. 

  13. Example: • If is angle A is acute, then angle A is less than 90 degrees. • Angle B is acute. • Angle B is less than 90 degrees.

  14. You Try: • If an angle measures more than 90 degrees, then it is not acute. • The measure of angle ABC is 120 degrees.

  15. Angle ABC is not acute.

  16. You Try: • If two lines will never intersect, then they are parallel • Lines AB and CD never intersect.

  17. Lines AB and CD are parallel.

  18. Law of Syllogism: • Example: • If you wear school colors, then you have school spirit • If you have school spirit, then your team feels great. • If you wear school colors, then your team feels great

  19. Example: • If you study hard, then you will do well in your classes. • If you do well in your classes, then you will graduate. • If you study hard, then you will graduate.

  20. Example: • If angle 2 is acute, then angle 3 is obtuse. • If angle 3 is obtuse, then angle 4 is acute. • If angle 2 is acute, then angle 4 is acute.

  21. You Try: • If a=bd, then c=fd • If c=fd, then d=oh

  22. If a = bd, then d = oh.

  23. You Try: • If jlt, then pql • If pql, then jtw

  24. If jlt, then jtw.

  25. Use Inductive and deductive reasoning: • Example: Make a conclusion about the sum of 2 even integers. • STEP 1: Inductive Reasoning • Pick a few samples: -2+4=2 ; 8+6=14 • Conjecture: even# + even # = even# • STEP 2: Deductive Reasoning • Use logic to prove your conjecture (first write a ‘let’ statement • Letn and m equal any integer

  26. PROOF 2n is even; 2m is even 2n+2m is the sum of even numbers 2n+2m= 2(n+m) 2(n+m) is even 2(n+m) was the sum of 2n+2m even #+even# = even # REASON b/c multiplying by 2 makes it an even number Addition factoring b/c multiplied by 2 makes an even number 3rd bullet 2n+2m=2(n+m) b/c 2n is even, 2m is even, 2(n+m) is even, and 2n+2m=2(n+m)

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