2.1 Conditional Statements Ms. Kelly Fall 2010

Standards/Objectives: Students will learn and apply geometric concepts. Objectives: Recognize the hypothesis and the conclusion of an if-then statement State the converse of an if-then statement Use a counterexample to disprove an if-then statement Understand the meaning of if and only if

Conditional Statement A logical statement with 2 parts: a hypothesis & conclusion Can be written in “if-then” form; such as, “If…, then…” Example: “If it rains after school, then I will give you a ride home.” Example: “If B is between A and C, then AB + BC = AC.”

Conditional Statement Hypothesis is the part after the word “If” Conclusion is the part after the word “then”

Ex: Underline the hypothesis & circle the conclusion. If you are a brunette, then you have brown hair. hypothesisconclusion Let’s try a few from our book…. Page 34 #1-6 Page 35 #1-6 Use a pencil and underline the hypothesis and double underline the conclusion. Work on these quietly in your group for 4-5 minutes, then compare answers.

Counterexample Used to show a conditional statement is false. It must keep the hypothesis true, but the conclusion false! It must keep the hypothesis true, but the conclusion false!

Ex: Find a counterexample to prove the statement is false. If x 2 =81, then x must equal 9. counterexample: x could be -9 because (-9) 2 =81, but x≠9.

You try… Here are four examples. Provide a counterexample on your own, then move around the room to find someone else who has the same counterexample as you. If ab < 0, then a < 0. If n2 = 5n, then n = 5. If a four-sided figure has four right angles, then it has four congruent sides. If a four-sided figure has four congruent sides, then it has four right angles.

Converse To write the converse, switch the hypothesis & conclusion parts of a conditional statement. Ex: Write the converse of “If you are a brunette, then you have brown hair.” If you have brown hair, then you are a brunette.

Using Biconditional Statements Conditional statements are not always written in the if-then form. Another common form of a conditional is only-if form. A biconditional statement is one that contains the phrase “ if and only if. ” Examples: “Segments are congruent if and only if their lengths are equal.”

Group exercise In your group, state the converse of each conditional, then tell whether it is true or false. If today is Friday, then tomorrow is Saturday. If x > 0, then x 2 > 0. If a number is divisible by 6, then it is divisible by 3. If 6x = 18, then x = 3.

3.6 Inductive Reasoning Using the Laws of Logic Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical argument. This differs from inductive reasoning, in which previous examples and patterns are used to form a conjecture.

Example on Inductive Reasoning Andrea knows that Robin is a sophomore and Todd is a junior. All the other juniors that Andrea knows are older than Robin. Therefore, Andrea reasons inductively that Todd is older than Robin based on past observations.

Example on inductive reasoning Look for a pattern and predict the next number in each sequence: 3, 6, 12, 24, ______ 11, 15, 19, 23, _____ 5, 6, 8, 11, 15, _____ Answers: 48 (Each number is twice the preceding number) 27 (Each number is 4 more than the preceding number) 20 (The difference in each number increases by 1)

Groupwork This will be collected and graded! Page Classroom Exercises 1-9 Written Exercises Put group names on back

HOMEWORK Page 35 #17-30