NAME DATE PERIOD. Inductive Reasoning and Conjecture , 5, 9 2 2, 4

Transcription

1 2-1 Skills Practice Inductive Reasoning and Conjecture Make a conjecture about the next item in each sequence , 1, 2, 5, , 1 1, 5, 9 2 2, , 4, 8, 16, 32 Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. 5. Points A, B, and C are collinear, 6. Point P is the midpoint of N Q. and D is between B and C. Lesson 2-1 A C D B N P Q 7. 1, 2, 3, and 4 form four linear pairs Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. 9. Given: ABC and CBD form a linear pair. Conjecture: ABC CBD 10. Given: A B, B C, and A C are congruent. Conjecture: A, B, and C are collinear. 11. Given: AB BC AC Conjecture: AB BC A B C 12. Given: 1 is complementary to 2, and 1 is complementary to 3. Conjecture: 2 3 Glencoe/McGraw-Hill 59 Glencoe Geometry

2 2-1 Make a conjecture about the next item in each sequence. 1. Practice Inductive Reasoning and Conjecture 2. 5, 10, 15, , 1, 1 2, 1 4, , 6, 3, 1.5, Make a conjecture based on the given information. Draw a figure to illustrate your conjecture. 5. ABC is a right angle. 6. Point S is between R and T. A R S T B C 7. P, Q, R, and S are noncollinear 8. ABCD is a parallelogram. and P Q Q R R S S P. P Q A B S R D C Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. 9. Given: S, T, and U are collinear and ST TU. Conjecture: T is the midpoint of S U. 10. Given: 1 and 2 are adjacent angles. Conjecture: 1 and 2 form a linear pair. 11. Given: G H and J K form a right angle and intersect at P. Conjecture: G H J K 12. ALLERGIES Each spring, Rachel starts sneezing when the pear trees on her street blossom. She reasons that she is allergic to pear trees. Find a counterexample to Rachel s conjecture. Glencoe/McGraw-Hill 60 Glencoe Geometry

3 2-2 Skills Practice Logic Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: q: Vertical angles are congruent. r: s: The sum of the measures of complementary angles is p and q 2. p r 3. p or s 4. r s 5. p q 6. q r Lesson 2-2 Copy and complete each truth table. 7. p q p p q ( p q) 8. T T T F F T F F p q q p q T T F T F T F T F F F T Construct a truth table for each compound statement. 9. q r 10. p r Glencoe/McGraw-Hill 65 Glencoe Geometry

4 2-2 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 60 seconds 1 minute q: Congruent supplementary angles each have a measure of 90. r: p q Practice Logic 2. q r 3. p q 4. p r Copy and complete each truth table. 5. p q p q p q 6. T T T F F T F F p q p p q p ( p q) T T T F F T F F Construct a truth table for each compound statement. 7. q (p q) 8. q ( p q) SCHOOL For Exercises 9 and 10, use the following information. The Venn diagram shows the number of students in the band who work after school or on the weekends. Work After School 5 3 Work Weekends How many students work after school and on weekends? 10. How many students work after school or on weekends? Glencoe/McGraw-Hill 66 Glencoe Geometry

5 2-3 Skills Practice Conditional Statements Identify the hypothesis and conclusion of each statement. 1. If you purchase a computer and do not like it, then you can return it within 30 days. 2. If x 8 4, then x If the drama class raises $2000, then they will go on tour. Write each statement in if-then form. 4. A polygon with four sides is a quadrilateral. 5. Those who stand for nothing fall for anything. (Alexander Hamilton) 6. An acute angle has a measure less than 90. Determine the truth value of the following statement for each set of conditions. If you finish your homework by 5 P.M., then you go out to dinner. Lesson You finish your homework by 5 P.M. and you go out to dinner. 8. You finish your homework by 4 P.M. and you go out to dinner. 9. You finish your homework by 5 P.M. and you do not go out to dinner. 10. Write the converse, inverse, and contrapositive of the conditional statement. Determine whether each statement is true or false. If a statement is false, find a counterexample. If 89 is divisible by 2, then 89 is an even number. Glencoe/McGraw-Hill 71 Glencoe Geometry

6 2-3 Practice Conditional Statements Identify the hypothesis and conclusion of each statement. 1. If 3x 4 5, then x If you take a class in television broadcasting, then you will film a sporting event. Write each statement in if-then form. 3. Those who do not remember the past are condemned to repeat it. (George Santayana) 4. Adjacent angles share a common vertex and a common side. Determine the truth value of the following statement for each set of conditions. If DVD players are on sale for less than $100, then you buy one. 5. DVD players are on sale for $95 and you buy one. 6. DVD players are on sale for $100 and you do not buy one. 7. DVD players are not on sale for under $100 and you do not buy one. 8. Write the converse, inverse, and contrapositive of the conditional statement. Determine whether each statement is true or false. If a statement is false, find a counterexample. If ( 8) 2 0, then 8 0. SUMMER CAMP For Exercises 9 and 10, use the following information. Older campers who attend Woodland Falls Camp are expected to work. Campers who are juniors wait on tables. 9. Write a conditional statement in if-then form. 10. Write the converse of your conditional statement. Glencoe/McGraw-Hill 72 Glencoe Geometry