Chapter 2 Test Review. Complete each truth table.
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1 1. Complete each truth table. 2. SCHOOL The Venn diagram shows the number of students in the band who work after school or on the weekends. 3. How many students work after school and on weekends? 4. How many students work after school or on weekends? Powered by Cognero Page 1
2 SUMMER CAMP Older campers who attend Woodland Falls Camp are expected to work. Campers who are juniors wait on tables. 5. Write a conditional statement in if-then form. 6. Write the converse of the conditional statement. Make a conjecture about each value or geometric relationship. 7. Point S is between R and T. 8. P, Q, R, and S are noncollinear and. 9. ABCD is a parallelogram. 10. ABC is a right angle. 11. 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. Write each statement in if-then form. 12. Those who do not remember the past are condemned to repeat it. (George Santayana) Powered by Cognero Page 2
3 13. Adjacent angles share a common vertex and a common side. Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. 14. If the moon has purple spots, then it is June. 15. If a and b are negative, then a + b is also negative. 16. If two triangles have equivalent angle measures, then they are congruent. Determine whether each conjecture is true or false. Give a counterexample for any false conjecture. 17. If 1 and 2 are adjacent angles, then 1 and 2 form a linear pair. 18. If and form a right angle and intersect at P, then. 19. If S, T, and U are collinear and ST = TU, then T is the midpoint of. Construct a truth table for each compound statement. 20. ~q (~p q) Powered by Cognero Page 3
4 21. q (p ~q) Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value. p: 60 seconds = 1 minute q: Congruent supplementary angles each have a measure of 90. r: < p q 23. q r 24. ~p ~r 25. ~p q Make a conjecture about the next item in each sequence , 10, 15, Powered by Cognero Page 4
5 28. 2, 1,,, , 6, 3, 1.5, 0.75 Identify the hypothesis and conclusion of each conditional statement. 30. If 3x + 4 = 5, then x = 3. Powered by Cognero Page 5
6 Answer Key If you are a junior, then you wait on tables. 6. If you wait on tables, then you are a junior. 7. RS + ST = RT 8. The segments form a square or a rhombus. or 9. AB = CD and BC = AD Sample answer: Rachel could be allergic to other types of plants that blossom when the pear trees blossom. 12. If you do not remember the past, then you are condemned to repeat it. Powered by Cognero Page 6
7 13. If two angles are adjacent, then they share a common vertex and a common side. 14. True; the hypothesis is false since the moon does not ever have purple spots. Since the hypothesis is false, the statement is always true. 15. True; when the hypothesis is true, the conclusion is also true, since the sum of two negative numbers is always negative. 16. False; two triangles can have the angle measures 30, 60, and 90, but one triangle can have side lengths 3, 4, and 5, and the second can have side lengths 6, 8, and 10. The hypothesis of the conditional is true, but the conclusion is false. This counterexample shows that the conditional statement is false. 17. False; 1 and 2 could each measure True 19. True seconds = 1 minute and congruent supplementary angles each have a measure of 90; true. 23. Congruent supplementary angles each have a measure of 90 or < 1; true seconds 1 minute and ; false seconds 1 minute or congruent supplementary angles each have a measure of 90; true Powered by Cognero Page 7
8 30. H: 3x + 4 = 5; C: x = 3 Powered by Cognero Page 8
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