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Honors Geometry 2-1 Inductive Reasoning & Conjecture 2-2 Logic 2-3 Conditional statements

Honors Geometry 2-1 Inductive Reasoning & Conjecture 2-2 Logic 2-3 Conditional statements. Vocabulary. If-then Statements Conditional Statements Hypothesis Conclusion Converse Inverse Contrapositive. Ex 1:.

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Honors Geometry 2-1 Inductive Reasoning & Conjecture 2-2 Logic 2-3 Conditional statements

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  1. Honors Geometry2-1 Inductive Reasoning & Conjecture2-2 Logic2-3 Conditional statements

  2. Vocabulary • If-then Statements • Conditional Statements • Hypothesis • Conclusion • Converse • Inverse • Contrapositive

  3. Ex 1: Change the conditional statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION. • Studying results in good grades

  4. Ex 1: Change the conditional statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION. • Studying results in good grades • If you study, then you will make good grades. • H: you study • C: you will make good grades Hypothesis/ConclusionDOES NOT include the If and Then

  5. You Try: Change the statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION • A polygon with six sides is a hexagon. Hypothesis/ConclusionDOES NOT include the If and Then

  6. You Try: Change the statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION • A polygon with six sides is a hexagon. • If a polygon has six sides, then it is a hexagon. • H: a polygon has six sides • C: it is a hexagon Hypothesis/ConclusionDOES NOT include the If and Then

  7. Changing a conditional statement • The three most common ways to change a conditional statement are by taking its: • Inverse, • Converse, or • Contrapositive. • In each case, either the hypothesis and the conclusion switch places, or a statement is replaced by its negation.

  8. Changing a conditional statement The sum of the measures of two complimentary angles is 90˚. • Conditional: • Converse: • Inverse: • Contrapositive:

  9. Changing a conditional statement The sum of the measures of two complimentary angles is 90˚. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. • Converse: • Inverse: • Contrapositive:

  10. Changing a conditional statement The sum of the measures of two complimentary angles is 90˚. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. • Converse: • If the sum of the measures of two angles is 90°, then the two angles are complimentary. • Inverse: • Contrapositive:

  11. Changing a conditional statement The sum of the measures of two complimentary angles is 90˚. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. • Converse: • If the sum of the measures of two angles is 90°, then the two angles are complimentary. • Inverse: • If two angles are not complimentary, then the sum of the measures of the two angles is not 90°. • Contrapositive:

  12. Changing a conditional statement The sum of the measures of two complimentary angles is 90˚. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. • Converse: • If the sum of the measures of two angles is 90°, then the two angles are complimentary. • Inverse: • If two angles are not complimentary, then the sum of the measures of the two angles is not 90°. • Contrapositive: • If the sum of the measures of two angles is not 90°, then the two angles are not complimentary.

  13. Changing a conditional statement STATE THE TRUTH VALUE OF EACH STATEMENT. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. • Converse: • If the sum of the measures of two angles is 90°, then the two angles are complimentary. • Inverse: • If two angles are not complimentary, then the sum of the measures of the two angles is not 90°. • Contrapositive: • If the sum of the measures of two angles is not 90°, then the two angles are not complimentary.

  14. Changing a conditional statement STATE THE TRUTH VALUE OF EACH STATEMENT. • Conditional: • If two angles are complimentary, then the sum of the measures of the two angles is 90°. TRUE • Converse: • If the sum of the measures of two angles is 90°, then the two angles are complimentary. TRUE • Inverse: • If two angles are not complimentary, then the sum of the measures of the two angles is not 90°. TRUE • Contrapositive: • If the sum of the measures of two angles is not 90°, then the two angles are not complimentary. TRUE

  15. Your turn. Write each statement and state its truth value. • Conditional: • If a polygon is a square, then it is a rectangle. • Converse: • Inverse: • Contrapositive:

  16. Your turn. Write each statement and state its truth value. • Conditional: • If a polygon is a square, then it is a rectangle. TRUE • Converse: • If a polygon is a rectangle, then it is a square. FALSE • Inverse: • If a polygon is not a square, then it is not a rectangle. FALSE • Contrapositive: • If a polygon is not a rectangle, then it is not a square. TRUE

  17. Ticket Out the Door: Write the If-Then Conditional, Converse, Inverse, and Contrapositive. “Those who do not remember the past are condemned to repeat it.” – George Santayana

  18. Ticket Out the Door: Write the If-Then Conditional, Converse, Inverse, and Contrapositive. “Those who do not remember the past are condemned to repeat it” – George Santayana • Conditional: • If you do not remember the past, then you are condemned to repeat it. • Converse: • If you are condemned to repeat it, then you do not remember the past. • Inverse: • If you do remember the past, then you are not condemned to repeat it. • Contrapositive: • If you are not condemned to repeat it, then you do remember the past.

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