Name ______Date ______Period ______
Geometry
Sections 2-1 to 2-3
Quiz Review
I. Write the symbolic notation for the following:
- Conditional: ______b. Converse: ______
c. Inverse: ______d. Contrapositive: ______
I. For each conditional, underline the hypothesis once and the conclusion twice.
1. If Tom studies, he will know the answers.
2. The sun is out if it is day time.
3. Allan likes to hang out with his friends.
II. Write the Converse, inverse and contrapositive of the conditional statement.
4.You will get a discount on your car insurance if you take drivers education classes.
Converse: ______
Inverse: ______
Contrapositive: ______
III. Rewrite the conditional in if-then form.
5. An object weighs one ton if it weighs 2000 pounds.
______
6. Blue trunkfish live in the waters of a coral reef.
______
IV. Fill in the blank.
7. A conditional statement is equivalent to its ______.
8. The ______of a conditional statement is found by switching the hypothesis and conclusion.
9. A(n) ______is a statement that contains the phrase “if and only if.”
10. If the statements p q and q r are true, then the statement p r is true by the Law of ______. If the statement p q is true and p is true, then q is true by the Law of ______.
V. Fill in the blank. Then draw a sketch that helps illustrate you answer.
11. If two lines intersect, then their intersection is ______point(s).
12. Through any ______points there exists exactly one line.
13. If two points lie in a plane, then the ______containing them lies in the plane.
14. If two planes intersect, then their intersection is a ______.
VII. Rewrite the biconditional statement as a conditional statement and its converse.
15. We will go to the beach if and only if it is sunny.
Conditional: ______
Converse: ______
16. A point on a segment is the midpoint of the segment if and only if it bisects the segment.
Conditional: ______
Converse: ______
VIII. Write the converse of each true conditional statement. If the converse is also true, combine the statements to write a true biconditional statement. Be sure to give a counterexample if the converse is false!
17. If you are in school, then it is a weekday.
Converse: ______
Biconditional: ______
18. If it rains, then there are clouds in the sky.
Converse: ______
Biconditional: ______
IX. Use the diagram to determine whether the statement is true or false.
______19. Points O, P, and Q are collinear.
______20. and are supplementary.
______21. Points M, P, and O lie in the same plane.
______22. is perpendicular to .
______23. is perpendicular to
______24. and are complementary.
______25. Point Q is between point O and point P.
X. Determine if statement (3) follows from statement (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.
- (1) If the measure of an angle is greater than , then it is obtuse.
(2) is greater than .
(3) is obtuse. ______
- (1) If Paul is taking History, then he will study World War II.
(2) Paul will study about World War II.
(3) Paul is taking History. ______
- (1) If Liz works after school, then she works in a candy store.
(2) Liz works after school.
(3) Liz works in a candy store. ______
- (1) If Sarah is reading, then she is reading a novel.
(2) If Sarah is reading a novel, then the book must be interesting.
(3) If Sarah is reading, then the book must be interesting. ______
XI. Determine if a valid conclusion can be reached from the two true statements using the Law of Detachment or the Law of Syllogism. If a valid conclusion is possible, state it and the law that was used. If a valid conclusion does not follow, write no conclusion.
30. (1) If Spot is a dog, then he has four legs.
(2) Spot has four legs.
______
Law of ______
31. (1) If Rachel lives in Tampa, then Rachel lives in Florida.
(2) If Rachel lives in Florida, then she lives in the United States.
______
Law of ______
- (1) If October 9 is a Tuesday, then October 10 is a Wednesday.
(2) October 9 is a Tuesday.
______
Law of ______
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