(1-4) Write a description of the pattern for each sequence. Use the pattern to show the next two terms.
1. 5, 11, 18, 26, …2. A, B, D, E, G, H, …
3. 3, 6, 12, 24, 48, …4. 1, 5, 30, 210, 1680, …
(5-6) Make a conjecture for each scenario. Show some examples to test your conjecture.
5. the square of an odd number6. The product of a multiple of 5 and a multiple of 2
(7-11) Find a pattern for each sequence. Use inductive reasoning to show the next two terms.
7. 3, 5, 9, 17, …8. 1, 4, 6, 24, 26, …
9. 1, –2, 2, –4, 0, …10. 11. 1, 1, 2, 3, 5, 8, 13, …
(12-13) Find one counterexample to show that each conjecture is false.
12. The sum of two integers is always positive.13. Vertical angles are never supplementary.
14. Patterns Draw the next two figures in the sequence shown below.
(15-16) Identify the hypothesis and conclusion of each conditional.
15. If the sidewalks are wet, then it has been raining.
16. The dog will bark if a stranger walks by the house.
(17-18)Write each sentence as a conditional.
17. A regular pentagon has exactly five congruent sides.18. All uranium is radioactive.
(19-20) Write a conditional statement that each Venn diagram illustrates.
19. 20.
(21-23) Write (and label) the converse, inverse, and contrapositive of the given conditional statements. Determine the truth value of all three statements. If a statement is false, give a counterexample.
21. If two angles are complementary, then their measures sum to 90.
22. If the temperature outside is below freezing, then ice can form on the sidewalks.
23. If a figure is a rectangle, then it has exactly four sides.
(24-26) Each conditional statement below is true. Write its converse. If the converse is also true,
combine the statements as a biconditional.
24. If a number is divisible by 2, then the number is even.
25. If two angles have the same measure, then the angles are congruent.
26. If x2 = 25, then x = 5.
(27-28) Write the two statements that form each biconditional.
27.Two lines are perpendicular if and only if they intersect to form four right angles.
28. A whole number is an odd number if and only if it is not divisible by 2.
(29-30) Is each statement below a good definition? If not, explain.
29. Two rays intersect if and only if they lie in the same plane.
30. A hexagon is a polygon with exactly six sides.