Name _____________________________ TEST - Chapter 2

Directions: Follow the directions for each section of the test. Show ALL work and circle your answers.

Part A. [1pt] Vocabulary. Place the correct term in each blank below. Do your best on spelling.

1__________________ - the ‘then’ part of the sentence

2__________________ - type of sentence joined by ‘and’

3__________________ - a sentence that is either true or false

4__________________ - another name for an informal proof where you write sentences (one after another) that explain the reasons why a statement is true

5__________________ - a chart of values showing all possibilities of a sentence being T or F

6__________________- valid form of reasoning that says “if p then q and if q then r are both true statements, then if p then r must also be true”

7__________________ - the ‘if’ part of the sentence

8__________________ - a sentence written in ‘if-then’ form

9__________________ - when reasoning by examples, this is your guess that describes the pattern

10__________________ - property where if a = b and b = c, then a = c

11__________________ - type of reasoning that uses a number of examples to arrive at a conclusion; following a pattern to come up with a rule

12__________________ - one false example that shows that a rule/pattern is incorrect

13__________________ - the related conditional written as “if q then p”

14__________________ - two or more sentences joined by the word ‘and’ or ‘or’

15__________________ - valid form of reasoning that says “if p then q is true and p is true, then q is true”

16__________________ - the related conditional written as “if ~q then ~p”

17__________________ - property where if a = b then b = a

18__________________ - type of reasoning using facts, rules, definitions, or properties to come to a conclusion

19__________________ - the related conditional written as “if ~p then ~q”

20__________________ - a sentence that is accepted as true without proof; similar to an axiom

21__________________ - another name for a formal proof where you write an organized list of statements and reasons to prove a theorem

22__________________ - property where a = a

23__________________ - type of sentence joined by ‘or’

24__________________ - another word for this symbol: v

25__________________ - to have the opposite meaning; to have the opposite truth value

26__________________ - another word for this symbol: ^

Part B. Make a conjecture about the next item in the sequence. EXPLAIN you reasoning!1. [2pts]

2. [2pts]

Part C. Determine if the conjecture is true of false. Give a counterexample for any false conjecture.3. [2pts] 4. [2pts]

If <1 and <2 are supplementary angles, then <1 and <2 are a linear pair.

Part D. [2pts] Create a truth table to show the following.5. ~p ^ q 6. ~ ( p v ~q )

Part E. Use the Venn Diagram below to answer the questions at the right.7. [1pt] How many people like to read poetry?

8. [1pt] What percentage of people like plays but not poetry or novels?

Part F. [1pt] Use the following statements to determine the truth value of the conjunction or disjunction. Show your work!

p: Mr. Hartmann teaches at Helfrich Park.

q: Helfrich Park does not lie in Indiana.

r: Indiana is in the United States.

8. r v ~p

9. ~q ^ p

Part G. [1pt] Identify the hypothesis and conclusion of the following statement.

10. If <1 and <2 are vertical angles, then they are congruent.

Part H. [3pts] Write each of the related conditionals based on the following true statement. Then determine the truth value of the related conditional.

** If you run ten miles tonight, you will be tired.

Name of related conditional Write the related conditional True or False? Conditional If you run ten miles today, you will be

tired tonight. TRUE

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Part I. [2pts] Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counter example.

14. If x2 = 25, then x = 5. 15. If pigs can fly, then 1 + 1 = 3.

Part J. [2pts] Deductive Logic. For the cases below, draw a conclusion based on (a) Law of Detachment or (b) Law of Syllogism. State which of these two reasons you used.

CASE CONCLUSION REASON16. If a whole number has a zero in the ones place, it is divisible by ten. If I am thinking of a whole number ending with a zero, then…..

17. If a hurricane is Category 5, then winds are greater than 155 miles per hour. If winds are greater than 155 miles per hour, then trees and signs are blown down. If a hurricane is Category 5, then…..

Part K. [1pt] Name the postulate that can be used to show each statement as true. Write the postulate number ONLY.

18. Planes O and M intersect in line r.

19. Since line AD lies in plane N, point E also lies in plane N.

20. Point F is also on line s through points D and K.

Part L. [1pt] Knowledge of geometric vocabulary and their definitions.21. Are the points D, F, and E coplanar? Explain.

Part M. [2pts] Create a Venn Diagram to show that the following conclusion is invalid. After the Venn Diagram, explain your reasoning.

22. Given: Some high school graduates choose to go on to college and get a Bachelor's Degree. Some who graduate college with a Bachelor's degree choose to continue and get a Master's Degree. John graduated from college and earned a Bachelor's Degree.

Conclusion: John has a Master's Degree.

23. Write an algebraic two column proof. Make sure you show each step.

24. Write a two column proof. Make sure you show each step.

25. Write a two column proof. Make sure you show each step.