Name_____________________________Period_________________________
Chapter 2 Exam
For each statement,
(a) write the converse,
(b) tell if the the converse is true or false.
(c) if true, write a biconditional. If false, write a counterexample .
1. If a polygon is a triangle, then it has three sides.
a) converse:__________________________________________________________________
_____________________________________________________________________________
b) True or False:_____________
c) biconditional or counterexample:_______________________________________________
____________________________________________________________________________
2. If George lives in Texas, then he lives in the United States.
a) converse:__________________________________________________________________
_____________________________________________________________________________
b) True or False:_____________
c) biconditional or counterexample:_______________________________________________
_____________________________________________________________________________
3. If it is Halloween then it is October 31.
a) converse:__________________________________________________________________
_____________________________________________________________________________
b) True or False:_____________
c) biconditional or counterexample:______________________________________________
____________________________________________________________________________
For Exercises 4-6 , name the property that justifies each statement.
4. If x  4  10 , then x  6 .________________________________
5. If
, then
6.
._________________________________
___________________________________________________________
7. By the Transitive Property of Congruence,
If
and
, then
_________________
8. Rewrite the following biconditional as two conditionals:
A quadrilateral is a rectangle if and only if it has four right angles.
1)_______________________________________________________________________
2)_______________________________________________________________________
Name_____________________________Period_________________________
9. Use the diagram at the right to find the measure of each angle.
a.
=____________
b.
=____________
c.
=____________
d.
=____________
e.
=____________
f.
= ____________
For Exercises 10–11, find the value of the variable in each diagram.
10.
x =_________________________
11.
x =___________________
12.
x=______________________________
For Exercises 13-14, explain why each statement is NOT a good definition.
13. Skew lines do not intersect.
14. A bird is an animal with wings.
Name_____________________________Period_________________________
For Exercises 15-19, use deductive reasoning to draw any possible conclusions. Write not possible if you cannot draw any conclusions.
15. If an animal is a snake, then it is a reptile.
“Gordon” is a reptile. Conclusion________________________________________
16. If Susan gets a hit this inning, then we will win.
Susan hits a triple.
Conclusion_________________________________________
17. If the bus is late, then we will be late for school.
If we are late for school, then we will receive a tardy penalty.
Conclusion__________________________________________
18. Christina is going to the dance with Dave or Tom.
She is not going to the dance with Tom
Conclusion_____________________________________________
19. If two angles are complementary, then the sum of their measures is 90.
Two angles have a measure sum of 124.
Conclu-
sion__________________________________________
20. Some figures that are piggles are shown below, as are some nonpiggles.
Tell whether each of the following is a piggle.
a)
b)
For problems 21-22, give a reason for each step.
21. Solve for x in the equation :
a.
________
b. ___________________________
c. ___________________________
d. ___________________________
22. Give a reason for each step.
Given: M is the midpoint of AB.
1) AM = MB
A
5x + 2
2)______________________
3) 5x = 12 – x
3)______________________
4) 6x = 12
4)______________________
23.
14 - x
B
1) ______________________
2) 5x + 2 = 14 – x
5) x = 2
M
5)______________________
By the Symmetric property of congruence: If
AB  XY , then ________________________.