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Honors Geometry 2.1/2.3 Inductive and Deductive Reasoning Practice Name: ____________________________________ Describe a pattern in the numbers. Write the next number in the pattern. 1. _______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ 2. 2, 5, 11, 23 _______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ Make a conjecture about each value or geometric relationship. 3. The relationship between AP and PB, if M is the midpoint of AB and P is the midpoint of AM. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 4. The product of three negative numbers. _______________________________________________________________________________________________ _______________________________________________________________________________________________ Decide whether each conjecture is true or false. If false, find a counterexample. 5. The quotient of two whole numbers is a whole number. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 6. The square root of a number x is always less than x. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 7. If a ray intersects a segment at its midpoint, then the ray is perpendicular to the segment. _______________________________________________________________________________________________ _______________________________________________________________________________________________ Determine if Statement 3 follows from the Statements 1 and 2 by either the Law of Detachment or Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 8. (1) If an angle measures more than 90 , then it is not acute. (2) (3) is not acute. 9. (1)All 45 angles are congruent. (2) (3) and are 45 angles. 10. (1)If (2) If (3) If is acute, then is obtuse. is obtuse, then is acute. is acute, then is acute. Make a valid conclusion based on the given statements if possible. If a conclusion can be drawn, then name the law of logic that was applied. 11. If you order the apple pie, then it will be served with ice cream. Matthew ordered the apple pie. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 12. If you wear the school colors, then you have school spirit. If you have school spirit, then the team feels great. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 13. If you eat too much turkey, then you will get sick. Kinsley got sick. _______________________________________________________________________________________________ _______________________________________________________________________________________________ 14. If an angle is not right, then its measure is between 90° and 180°. A is not right. _______________________________________________________________________________________________ _______________________________________________________________________________________________ Determine whether or not the given conditional and its converse are true. Use this information to write a biconditional statement if it is appropriate. If not, explain why it is not appropriate. 15. If it is Wednesday, then it is not Thursday. Is conditional true or false? ___________________ , Is converse true or false? ___________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ 16. If two lines intersect to form a right angle, then they are perpendicular. Is conditional true or false? ___________________ , Is converse true or false? ___________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ _______________________________________________________________________________________________ Write the biconditional as a conditional and its converse. Then determine whether the biconditional is true or false. If false, give a counterexample. 17. Two angles are supplementary if and only if the sum of their measures is 180°. Conditional:______________________________________________________________________________________ Converse:_______________________________________________________________________________________ Is biconditional true or false? _________________ Counter example (if needed): _______________________________________________________________________________________________ _______________________________________________________________________________________________ Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional. If the converse is false, provide a counterexample. 18. Complementary angles are two angles whose measures sum up to 90°. Conditional:______________________________________________________________________________________ Converse: _______________________________________________________________________________________ Biconditional or Counterexample: _______________________________________________________________________________________________ _______________________________________________________________________________________________ Rewrite the following statement as a conditional and its converse. If the converse is true, write its biconditional. If the converse is false, provide a counterexample. 19. Vertical angles are congruent. Conditional: _____________________________________________________________________________________ Converse: _______________________________________________________________________________________ Biconditional or Counterexample: _______________________________________________________________________________________________ _______________________________________________________________________________________________