Name_____________________________Period_________________________
Chapter 2 Exam
For each statement, (a) write the converse, (b) decide whether 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 two angles are vertical angles, then they are congruent.
a) converse:__________________________________________________________________
_____________________________________________________________________________
b) True or False:_____________
c) biconditional or counterexample:______________________________________________
____________________________________________________________________________
For Exercises 4-6 , name the property that justifies each statement.
4. If
, then
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.
x=_________________________
10.
11.
x =___________________
For Exercises 12–13, use deductive reasoning to draw any possible conclusions. Write not possible if you cannot draw any conclusions.
12. If an animal is a snake, then it is a reptile.
“Gordon” is a reptile.
Conclusion________________________________________
13. If Susan gets a hit this inning, then we will win.
Susan hits a triple.
Conclusion_________________________________________
14. 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__________________________________________
15. If two angles are complementary, then the sum of their measures is 90.
m
16.
+
=124.
Conclusion__________________________________________
is five times as large as its complement m∠B. Find m∠A.
Name_____________________________Period_________________________
For Exercises 17-19, determine whether each statement is a good definition. If it is not, provide a counterexample.
17. Congruent angles have the same measure.
18. Supplementary angles are two angles whose measures add up to 180.
19. A bird is an animal with wings.
20. Some figures that are piggles are shown below, as are some nonpiggles.
Tell whether each of the following is a piggle.
a)
b)
21. Give a reason for each step.
Given________
a. ___________________________
b. ___________________________
c. ___________________________
22. Give a reason for each step.
M is the midpoint of AB.
1) AM = MB
A
5x + 2
1) ______________________
2) 5x + 2 = 14 – x
2)______________________
3) 5x = 12 – x
3)______________________
4) 6x = 12
4)______________________
5) x = 2
5)______________________
Find the value of x.
23.
M
14 - x
B