1. Lesson 2-1 Conditional Statements 1 Lesson 2-3 Conditional Statements

2. Lesson 2-1 Conditional Statements 2 Conditional Statement Definition:A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Example:If we practice hard, then we will win tomorrow. Continued……

3. Lesson 2-1 Conditional Statements 3 Conditional Statements have 2 parts: The hypothesis follows the word “if”. It is the given information or the condition. The conclusion follows the word “then”. It is the result of the given information. If a polygon has six sides, then it is a hexagon. Example 1: Hypothesis Conclusion

4. Lesson 2-1 Conditional Statements 4 Writing Conditional Statements When writing conditional statements, turn the subject into the hypothesis and the predicate into the conclusion. Example 1: Vertical angles are congruent. If two angles are vertical, then they are congruent. Conditional Statement: Example 2: Adjacent angles have a common side. Conditional Statement: If two angles are adjacent, then they have a common side.

5. Lesson 2-1 Conditional Statements 5 If …Then vs. Implies Two angles are vertical implies they are congruent. Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent.

6. Lesson 2-1 Conditional Statements 6 Logic Symbols p: hypothesis q: conclusion p  q: If “hypothesis”, then “conclusion”. ~: “not” : “and” (conjunction) : “or” (disjunction) : “therefore”

7. Lesson 2-1 Conditional Statements 7 Forms of Conditional Statements Conditionalpqpq Converseqpqp Inverse~p  ~q Contrapositive~q  ~p

8. Lesson 2-1 Conditional Statements 8 Converse Switch the hypothesis and conclusion (q  p) p  q If two angles are vertical, then they are congruent. q  p If two angles are congruent, then they are vertical. Continued…..

9. Lesson 2-1 Conditional Statements 9 Inverse State the opposite of both the hypothesis and conclusion. (~p  ~q) p  q : If two angles are vertical, then they are congruent. ~p  ~q: If two angles are not vertical, then they are not congruent.

10. Lesson 2-1 Conditional Statements 10 Contrapositive Switch the hypothesis and conclusion and state their opposites. (~q  ~p) p  q : If two angles are vertical, then they are congruent. ~q  ~p: If two angles are not congruent, then they are not vertical.

11. Lesson 2-1 Conditional Statements 11 More about Contrapositives Contrapositives are logically equivalent to the original conditional statement. If p  q is true, then  q  p is true. If p  q is false, then  q  p is false.

12. Lesson 2-1 Conditional Statements 12 Biconditional When a conditional statement and its converse are both true. Use the phrase if and only if (sometimes abbreviated: iff) to combine the two statements. Statement: If an angle is right, then it has a measure of 90 . Converse: If an angle measures 90 , then it is a right angle. Biconditional: An angle is right if and only if it measures 90 .