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Conditional Statements

Conditional Statements. Wednesday, October 19. Correct Homework. See Post-It Note on board for solutions to. Objective, Agenda, Homework. Objective * analyze statements in if-then form *write the converse, inverse, and contrapositive of if-then statement

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Conditional Statements

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  1. Conditional Statements Wednesday, October 19

  2. Correct Homework See Post-It Note on board for solutions to

  3. Objective, Agenda, Homework • Objective * analyze statements in if-then form *write the converse, inverse, and contrapositive of if-then statement *use deductive reasoning to draw conclusions • Agenda • Correct and Turn-In Worksheet • Conditional Statements and Practice • Exit Slip • Homework • * 2.3 pg 78 (18-26 even, 34, 38, 40, 42, 46-47)

  4. Notes: Definitions Take out a piece of paper and a pencil to take the following notes

  5. Conditional Statement • A conditional statement is a statement that can be written in if-thenform • Why is this important? • Advertisers often lure consumers into purchasing expensive items by convincing them that they are getting something for free in addition to their purchase. • Examples • Sign-up for a Six-Month Fitness Plan and Get 6 Months FREE • Get $1500 Cash back when you buy a NEW car • FREE phone with every one-year service enrollment • Re-write Examples in if-then form • If you buy a car, then you get $1500 cash back • Now you try writing the other 2 in if-then form

  6. Parts and Symbols of an If-Then Statement • If-then statement is written in the form • If p, then q • The “p,” or the phrase after the word if is the hypothesis • The “q,” or the phrase after the word then is the conclusion • Symbols to know: pq • Read “if p, then q” • Or “p implies q”

  7. Identify Hypothesis and Conclusion First, write in the if-then form. Then identify the hypothesis and conclusion • Example: The Tigers will play in the tournament if they win their next game. • If-then form: If the Tigers win their next game, then they will play in the tournament. • Hypothesis: the Tigers win their next game • Conclusion: they will play in the tournament

  8. Identify Hypothesis and Conclusion First, write in the if-then form. Then identify the hypothesis and conclusion A 32-ounce pitcher holds a quart of liquid. The sum of the measures of supplementary angles is 180. An angle formed by perpendicular lines is a right angle.

  9. Identify Hypothesis and Conclusion First, write in the if-then form. Then identify the hypothesis and conclusion • A 32-ounce pitcher holds a quart of liquid. • If a pitcher holds a 32 ounces of liquid, then it holds a quart of liquid. • The sum of the measures of supplementary angles is 180. • If sum of measures of angles are 180, then they are supplementary angles. • An angle formed by perpendicular lines is a right angle. • If the angle formed by two lines is right, then the lines are perpendicular.

  10. Construct Other Types of Statements With your partner use the cards to construct other types of statements.

  11. Construct Other Types of Statements With your partner use the cards to construct other types of statements. Arrange the cards in the conditional form Formed by given hypothesis and conclusion If p, then q. Write this example of conditional form in your notes: If two angles have the same measure, then they are congruent.

  12. Construct Converse Statement A converse statement is formed by exchanging the hypothesis and conclusion of the conditional With your partner construct a converse statement using your cards Write the converse of: If two angles have the same measure, then they are congruent.

  13. Converse Instead of if p, then q a converse statement is if q, then p. If two angles are congruent, then they have the same measure.

  14. Construct Inverse Statement An inverse statement is formed by Negating both the hypothesis and conclusion of the conditional With your partner construct an inverse statement using your cards Write the inverse of: If two angles have the same measure, then they are congruent.

  15. Inverse Instead of if p, then q an inverse statement is if not p, then not q. If two angles do not have the same measure, then they are not congruent.

  16. Construct Contrapositive Statement A contrapositive statement is formed by Negating both the hypothesis and conclusion of the converse statement With your partner construct an contrapositive statement using your cards Write the contrapositive of: If two angles have the same measure, then they are congruent.

  17. Contrapositive Instead of if p, then q a converse statement is if not q, then not p. If two angles are not congruent, then they do not have the same measure

  18. Write the converse, inverse, and contrapositive • Conditional: If a polygon is a rectangle, then it is a square • Hypothesis • Conclusion • Converse: • Inverse: • Contrapositive

  19. Write the converse, inverse, and contrapositive • Conditional: If a polygon is a rectangle, then it is a square • Hypothesis: a polygon is a rectangle • Conclusion: a polygon is a square • Converse: If a polygon is a square, then in is a rectangle. • Inverse: If a polygon is not a rectangle, then it is not a square. • Contrapositive If a polygon is not a square, it is not a rectangle. Decide which of the above statements is true and which is false.

  20. Homework * 2.3 pg 78 (18-26 even, 34, 38, 40, 42, 46-47)

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