Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Geometry Name: _______________________________ Unit 1: Lesson 1.5 Date: _________________ Period: _______ Conditional Statements Essential Questions: o Why are some statements bi-conditional and other statements are not? Goal: I will understand that a relationship exists between the hypothesis and conclusion of a conditional statement. Key Ideas/Vocabulary: CONDITIONAL STATEMENT a ________ statement that involves a comparison of _______ or _________ (a.k.a IF-THEN STATEMENT) A conditional statement has two parts: the hypothesis (p) and the conclusion (q). “If p, then q.” Symbol: pq CONVERSE is formed by interchanging the hypothesis and conclusion in the conditional statement. “If q, then p.” Symbol: q p “A converse and conditional statement can be ________ or __________.” COUNTEREXAMPLE at least one fact or argument that indicates a mathematical theorem is NOT true. BI-CONDITIONAL a conditional and its converse where the converse is also true. “if and only if” Example: “A right angle is an angle that measures 900.” Symbol: pq Section 1: Conditional Statements and Converses 1) Identify the hypothesis and conclusion of each YT 1) Identify the hypothesis and conclusion of statement. Then write each statement in if-then each statement. Then write each statement in ifform. then form. “Every student who takes geometry in Mr. Marttila’s class “School begins only if it is 7:30 A.M.” gets an A on the Geometry Test” Answer: Answer: If-Then Statement:_________________________ 2) Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form. “A five-sided polygon is a pentagon” Answer: If-Then Statement:_________________________ YT 2) Identify the hypothesis and conclusion of each statement. Then write each statement in ifthen form. “To find the distance between two points, you can use the Distance Formula” Answer: If-Then Statement:________________________ If-Then Statement:_________________________ Section 2: Converse and Bi-conditionals 3) Write the converse and bi-conditional of the statement. “If the date is July 4th, then it is Independence Day.” YT 3) Write the converse and bi-conditional of the statement. “If you visited the Statue of Liberty, then you’ve been to New York.” Answer: Answer: Converse:_________________________________ Converse:_________________________________ Bi-Conditional:_____________________________ Bi-Conditional:_____________________________ Section 3: Truth Values of Conditional Statements and Converses 4) Decide whether the statement and its YT 4) Decide whether the statement and its converse are true. converse are true. If mA 30 , then A is acute. If it lives in water, then it is a fish. Answer: Answer: CONDITIONAL TRUE OR FALSE CONVERSE TRUE OR FALSE 5) Decide whether the statement and its converse are true. If two lines intersect, then they are not parallel. Answer: CONDITIONAL TRUE OR FALSE CONVERSE TRUE OR FALSE Section 4: Writing a Counterexample 6) Write a counterexample to show that the following conditional statement is false. If 2 x 2 x 3 0 , then x 1. Answer: CONDITIONAL CONVERSE TRUE OR FALSE TRUE OR FALSE YT 5) Decide whether the statement and its converse are true. If you have vertical angles, then the angles are congruent. Answer: CONDITIONAL TRUE OR FALSE CONVERSE TRUE OR FALSE YT 6) Write a counterexample to show that the following converse of the conditional is false. If the number is divisible by 3, then the number is odd. Answer: 7) Section 5: Using Postulates Use the diagram at the right to give examples of Postulates 5 through 11. Homework: Conditional Statements – Supplement Worksheet # 7 Lesson Summary: Translate one of the Postulates 5, 6, 8, or 9 to “if-then” form Name______________________________________________Period__________Date____________________ CONDITIONAL STATEMENTS - SUPPLEMENT WORKSHEET # 7 USE THE CONDITIONAL STATEMENT TO ANSWER QUESTIONS 1 – 3. If you like the Phillies, then you like Baseball. 1.) Underline the hypothesis of this statement. 2.) Circle the conclusion of this statement. 3.) Write the converse of the statement: ____________________________________________________________________ USE THE CONDITIONAL STATEMENT TO ANSWER QUESTIONS 4– 6. If you listen to One Direction, then you like pop rock. 4.) Identify the hypothesis:_____________________________________________ 5.) Identify the conclusion:_____________________________________________ 6.) Write the converse of the statement: ____________________________________________________________________ 7.) Use the given information to write a conditional statement: Hypothesis: You have perpendicular lines Conclusion: you have 4 right angles ____________________________________________________________________ 8.) Use the given information to write a conditional statement: Hypothesis: You have two angles Conclusion: the angles are supplementary ____________________________________________________________________ 9.) Write a conditional statement regarding an isosceles triangle. ____________________________________________________________________ 10.) Write a conditional statement regarding an obtuse triangle. Then the converse. Conditional:___________________________________________________________ Converse:_____________________________________________________________ 11.) Write a bi-conditional statement regarding a scalene triangle. ____________________________________________________________________ 12.) Write a bi-conditional statement regarding a Disney character. ____________________________________________________________________ 13.) Find a counterexample for the statement. “If you play a musical instrument then you are in the school band.” ____________________________________________________________________ 14.) Find a counterexample for the statement. “If you don’t eat beef, then you are a vegetarian.” ____________________________________________________________________ 15.) Find a counterexample for the statement. If 6x – 3 > 1, then x > 2. ____________________________________________________________________ 16.) Find a counterexample for the statement. If today is Sunday, you go to school tomorrow. ____________________________________________________________________ 17.) Find a counterexample for the converse of the conditional statement. If u > -5, then u is a positive. ____________________________________________________________________