2-1 Conditional Statements M11.B.2 Objectives: 1) To recognize conditional statements. 2) To write converses of conditional statements.

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2-1 Conditional Statements M11.B.2 Objectives: 1) To recognize conditional statements. 2) To write converses of conditional statements.

Vocabulary Another name for an if-then statement is a conditional. 2 Parts of the Conditional 1) Hypothesis “if” 2) Conclusion “then”

Example: Identify the Hypothesis & Conclusion If two lines are parallel, then the lines are coplanar. Hypothesis: Conclusion:

Example Identify the hypothesis and the conclusion. 1. If y-3=5, then y=8. 2. If today is the first day of fall, then the month is September.

Example: Writing a Conditional 1) An acute angle measures less than 90. 2) A triangle has three sides.

Vocabulary A conditional can have a truth value of true or false. True: Every time the hypothesis is true, the conclusion is true. False: Hypothesis is true but the conclusion is false. Counterexample – An example or instance that makes a statement false.

Example: Find a counterexample  Conditional False 1) If x ≥0, then x ≥ 0 2) If you play a sport with a ball and a bat, then you play softball. 2

Example: Using a Venn Diagram 1) If you live in Hazleton, then you live in PA. 2) If something is a dolphin, then it is a mammal.

Vocabulary The converse of a conditional switches the hypothesis and the conclusion.

Example: Write the converse of the following conditional 1) If x = 9, then x + 3 = 12. 2) If two lines intersect to form 90, then they form a right angle.

Example: Finding the truth value of a Converse 1) Write the converse of each conditional and determine the truth value of each. Conditional: If a figure is a square, then it has four sides. Converse:

Using Symbols… In symbolic form, the letter “p” stands for hypothesis and the letter “q” stands for the conclusion. COPY THE ORANGE BOX ON PAGE 70 INTO YOUR NOTEBOOKS!

Example - Summary Write the statement “All dogs are mammals” as a conditional and then write the converse. Determine the truth value of each statement.