Conditional Statements in Geometry: Understanding Hypotheses and Conclusions
Learn about conditional statements in geometry, including identifying hypotheses and conclusions, finding counterexamples, writing converses, and using Venn diagrams to visualize relationships. Explore examples and vocabulary related to 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.
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.
