1. Geometry 2-6 Review Problems Unit 2 – Reasoning and Proof

2. Review Problems Write each sentence as a conditional statement Today is Monday if yesterday was Sunday. If yesterday was Sunday, then today is Monday. 1

3. Review Problems Write each sentence as a conditional statement A number is divisible by 4 if it is divisible by 8. If a number is divisible by 8, then it is divisible by 4. 2

4. Review Problems A student on the high honor roll has at least a 90 average. Write each sentence as a conditional statement Bert goes shopping for groceries only on Wednesday. If Bert goes shopping for groceries, then it is Wednesday. If a student is on the high honor roll, then the student has at least a 90 average. 3

5. Review Problems For each statement, write the converse, and decide whether the converse is true or false. If George lives in Texas, then he lives in the United States. If two angles are vertical angles, then they are congruent. If George lives in the United States, then he lives in Texas. False If two angles are congruent, then they are vertical angles. False 4

6. Review Problems For each statement, write the converse, and decide whether the converse is true or false. If a polygon is a pentagon, then it has five sides. If Mary lives in Minneapolis, then she lives in Minnesota. If a polygon has five sides, then it is a pentagon. True If Mary lives in Minnesota, then she lives in Minneapolis False 5

7. Review Problems Show that the conditional statement is false All vegetables are carrots. A point may lie on at most two lines. Broccoli is a vegetable A point may lie on three intersecting lines 6

8. Review Problems Give a counterexample that demonstrates that the converse of the statement is false. If you live in Detroit, then you live in Michigan. You could live in Ann Arbor If an animal is a leopard, then it has spots. Dalmations 7

9. Review Problems Write the converse of each true statement. If the converse is also true, combine the statements to write a true biconditional statement. If the statement is not true, show that it is false. Converse is false, Point C could be beyond B 8

10. Review Problems Write the converse of each true statement. If the converse is also true, combine the statements to write a true biconditional statement. If the statement is not true, show that it is false. 9

11. Review Problems Write a conclusion using the true statements. If no conclusion is possible, write no conclusion. If Jay doesn’t work hard, then he won’t start the game and will quit the team. Jay quit the team. no conclusion If two planes intersect, then their intersection is a line. Plane A and plane B intersect. Plane A and plane B intersect in a line. 10

12. Review Problems Write a conclusion using the true statements. If no conclusion is possible, write no conclusion. If Hank applies for the job, then he will be the new lifeguard at the pool. If he is the new lifeguard at the pool, then he will buy a new car. Hank applies for the job. Hank will buy a new car. If Tim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Tim gets stung by a bee. Tim will go to the hospital. 11

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19. Review Problems 18

20. Review Problems Solve for X 19

21. Review Problems Solve for X 20

22. Review Problems Solve for X 21

23. Review Problems Solve for X 22

24. Review Problems Solve for X 23

25. Review Problems 24

26. Review Problems 25

27. Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. If yesterday was Sunday, then today is Monday. If a number is divisible by 8, then it is divisible by 4. If Bert goes shopping for groceries, then it is Wednesday. If a student is on the high honor roll, then the student has at least a 90 average. If George lives in the United States, then he lives in Texas. False If two angles are congruent, then they are vertical angles. False If a polygon has five sides, then it is a pentagon. True If Mary lives in Minnesota, then she lives in Minneapolis False Broccoli is a vegetable A point may lie on three intersecting lines You could live in Ann Arbor Dalmations Converse is false, Point C could be beyond B no conclusion Plane A and plane B intersect in a line. Hank will buy a new car. Tim will go to the hospital.

28. Answers 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.