1 / 18

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:.

bwilson
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related