1 / 20

Section 2-2

Learn about biconditional statements in geometry that contain the phrase "if and only if," their interpretations, and examples with conditionals and converses.

lawsonbrian
Download Presentation

Section 2-2

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. Section 2-2 Biconditional Statements

  2. Biconditional statement • a statement that contains the phrase “if and only if”. • Equivalent to a conditional statement and its converse.

  3. We can use iff to stand for “If and only if”

  4. In order for a biconditional statement to be TRUE, both the conditional statement and its converse must be true.

  5. Two lines intersect if and only if their intersection is exactly one point. Example #1: Write this biconditional statement as a conditional statement.

  6. Conditional Statement: • If two lines intersect, then • their intersection is exactly • one point. True

  7. Now write the converse. • If their intersection is exactly one point, then two lines intersect. True

  8. Example #2 Write this biconditional statement as a conditional statement. • Three lines are coplanar if and only if they lie in the same plane.

  9. If three lines are coplanar, then they lie in the same plane. Conditional Statement: True

  10. If three lines lie in the same plane, then they are coplanar. Now write the converse. True

  11. Write the conditional as a biconditional statement. • If an angle is acute then it has a measure between 0° and 90°.

  12. Write the converse • If an angle has a measure between 0° and 90°, then it is acute. True

  13. Identify whether the converse is true or false • If it is true, then a biconditional can be written • If it is false, then a biconditional CAN NOT be written.

  14. Bicondtional: • An angle is acute if and only if it has a measure between 0° and 90°.

  15. Write the conditional as a biconditional statement. • If an animal is a leopard, then it has spots. Write the converse. • If an animal has spots, then is a leopard. False

  16. Therefore a biconditional for this statement does not exist!

  17. More Examples: Write each conditional as a biconditional statement, if possible. Be sure to give a counterexample if the converse is false! Try It!

  18. If is perpendicular to , then their intersection forms a right angle. Converse: If, and intersect at a right angle, then they are perpendicular to each other. True

  19. Biconditional: • is perpendicular to iff their intersection forms a right angle.

  20. Counterexample: • let then 2. If x2 < 49, then x < 7 If x < 7, then x2 < 49. Converse: Therefore, a biconditional can not be written!

More Related