2-1 – If-Then Statements; Converses

1. 2-1 – If-Then Statements; Converses

2. Conditional Statement • Conditional Statement a.k.a. _____________ • Often written in ________________ form • Examples: If _________, then _________. ______________________

3. Conditional Statement • Other forms: __________ implies __________ __________ only if __________ __________ if __________

4. Examples In each of the following conditionals, underline the hypothesis once and the conclusion twice (or highlight). • if B is the midpoint of . • We will go only if it is sunny. • is a right angle implies . • If , then .

5. Converse/Counterexample • What is the converse of a conditional statement? • Example: • Conditional Statement: If ______, then ______. • Converse: If ______, then ______. • What is a counterexample?

6. Examples Tell whether each statement is true or false. Then write the converse and tell whether it is true or false. If the statement or the converse is false, give a counter example. • If two angles are right angles, then they are congruent. Converse: Counterexample: • implies . Converse: Counterexample:

7. Examples (Cont.) • If a number is divisible by 2, then it is divisible by 4. Counterexample: Converse: • An animal is a penguin only if it is a bird. Converse: Counterexample:

8. Biconditional • What is a biconditional? • Example: • Conditional Statement: If ______, then ______. • Converse: If ______, then ______. • Biconditional: ______ if and only if ______.

9. Examples Write each biconditional as two conditions that are converses of each other. • An angle is a right angle if and only if its measure is 90. Statement: Converse: • if and only if . Statement: Converse: • B is on if and only if B is on and . Statement: Converse:

10. 2-2 – Properties from Algebra

11. Properties of Equality Addition Property: If _________________, then _________________. If _____________and_____________, then __________________________. Subtraction Property: If _________________, then _________________. If _____________________, then _____________________.

12. Properties of Equality Multiplication Property: If _________________, then _________________. If _________________, then _________________. Division Property: If _________________, then _________________. If ___________________, then ___________________.

13. Properties of Equality Substitution Property: If ______________ and ______________, then _________________. If _______________and_______________, then __________________________. Distributive Property: If _________________, then _________________. If _________________, then _________________.

14. Examples Justify each statement with a property from algebra, or a definition or postulate from geometry. • If and , then . • If , then . • If and , then . • If point B is in the interior of , then . • If , then .

15. Properties of Equality (numbers, variables, lengths, angle measures) Reflexive Property: _________ = _________ _________ = _________ Symmetric Property: If _________________, then _________________. If _____________________, then _____________________. Transitive Property: If _________________and_________________, then _________________.

16. Properties of Congruence (segments, angles, polygons) Reflexive Property: _________ _________ _________ _________ Symmetric Property: If _________________, then _________________. If _________________, then _________________. Transitive Property: If _________________and_________________, then _________________.

17. Complete the following proofs by supplying the missing statements and reasons. • Given: ; Prove: K P R S T V

18. Complete the following proofs by supplying the missing statements and reasons. • Given: Prove: 3 1 2 4

19. Complete the following proofs by supplying the missing statements and reasons. E A • Given: Prove: I 1 2 3 U O