Chapter 2 Review
Name_____________________
Determine the next THREE numbers in the pattern and clearly explain how the pattern continues.
1.
–12,–8,–4,0,...
2.
3,–9,27,–81,...
3.
100, 101, 98, 103, 96, 105,…
4.
2, 8, 32, 128,…
Write the original conditional, the converse, the inverse, and the contrapositive of the following
statements. Circle whether each statement is true or false. If false, give a counterexample to verify
your conclusion.
5. “Basketball players are athletes.”
Conditional:
True/False
Converse:
True/False
Inverse:
True/False
Contrapositive:
True/False
6. “A regular polygon has congruent sides”
Conditional:
True/False
Converse:
True/False
Inverse:
True/False
Contrapositive:
True/False
7. Write “An angle with a measure between 90o and 180o is called obtuse” as a biconditional
and explain what makes it a valid biconditional statement.
Solve the following equations. Provide reasons for each step.
8. 4(2x+ 11) = 76
9. 14(x + 1) = –7(4 + x)
In 10-13, determine if the statement be assumed true from the diagram. Explain your reasoning.
10. BAC and CAD are supplementary.
11. BAC  BAE
12. CE  BD
13. CE bisects BD
14. Identify a relationship between any three points in the diagram above. Explain your reasoning.
15. What angle pair relationships can you assume from the diagram above?
16. If A is acute, then 0° < m A < 90°. Angle B is an acute angle. What conclusion can you
make? Explain, indicate which form of logical reasoning was used.
17. If B is between A and C, then AB + BC = AC. E is between D and F. What conclusion can you
make? Explain, indicate which form of logical reasoning was used.
18. If it is above 90oF outside, then Regina will wear shorts. Regina wore shorts. Does this mean it
is above 90o? Explain, indicate which form of logical reasoning was used.
19. Robotics Because robots can withstand higher temperatures than humans, a fire-fighting robot
is under development. Number the following statements about the robot in order. Then use the Law
of Syllogism to complete the statement, “If there is a fire, then __?__.”
_____If the robot sets off the fire alarm, then it concludes there is a fire.
_____If the robot senses high levels of smoke and heat, then it sets off a fire alarm.
_____If the robot locates the fire, then the robot extinguishes the fire.
_____If there is a fire, then the robot senses high levels of smoke and heat.
_____If the robot concludes there is a fire, then it locates the fire.
G
20. Given: D is the midpoint of CE
C is the midpoint of BD
Prove: BC=DE
A
F
21. Given: AB  BC , EF  FG ,
BD and FH are angle bisectors.
Prove: ABD  EFH
B
C
D
E