Download Good luck to: Date: Make sure you read each question carefully. The

Good luck to: _________________________________
Date: ______________________
Make sure you read each question carefully. The points are indicated by each problem.
I. Patterns. (5)
1. Sketch the fourth figure in the pattern below.
2. Write the next three numbers in the pattern… 0, 1, 3, 6, _____, ______, _______
II. Find the counterexample to disprove the conjecture. (5)
1. All intersecting planes form right angles.
___________________________________
_____________________________________________________________________________
2. The value of x3 is always greater than the value of x. ________________________________
______________________________________________________________________________
3. Regular polygons always have an even number of sides. _____________________________
______________________________________________________________________________
III. For the statement “Band members are musicians,” determine if each statement is true
or false. (2)
1. If you are not a musician, then you are not a band member.
True or False
2. If you are a musician, then you are a band member.
True or False
3. If you are not a band member, then you are not a musician.
True or False
4. If you are a band member, then you are a musician.
True or False
IV. Write the if-then statement, the converse, inverse and contrapositive for the following
statement… “A poet is a writer.” (5)
1. If-then: _________________________________________________________________
2. Converse: _______________________________________________________________
3. Inverse: _________________________________________________________________
4. Contrapostive: ___________________________________________________________
Geometry A
1
Ms. Busskohl
Good luck to: _________________________________
Date: ______________________
V. What kind of conclusions can you make using the statements and which law did you
use? If the statement is invalid then state that. (6)
1. If the light is on, then someone is home. The light is on. ________________________
Law: ______________________________
2. The Liberty Bell is located in Philadelphia, Pennsylvania. Rob has never been in
Pennsylvania. ___________________________________________________________
Law: _______________________________
3. If Estelle takes her broker’s advice, she’ll invest in stocks of Citibank. If Estelle invests
in stocks of Citibank, she’ll earn 50% on her investment by next year.
________________________________________________________________________
Law: _______________________________
4. If you mail the payment by noon, then it will arrive by tomorrow. If you payment arrives
by tomorrow, then you won’t be charged a late fee. ______________________________
________________________________________________________________________
Law: _______________________________
5. If two integers are added together, then the result is an integer. You add an integer. You
add an integer to another integer y. ___________________________________________
Law: _______________________________
6. If Lauren gets money she gives half of it to Danny. If Danny gets money he gives half of
it to Lauren. ____________________________________________________________
Law: _______________________________
VI. Decide whether the statement is a valid definition, if not, provide a more accurate
definition. (5)
1. If a polygon is not convex, then it is a concave polygon.__________________________
__________________________________________________________________________
2. If a figure is an n-gon, then it is a polygon with n-sides. ___________________________
___________________________________________________________________________
3. If two angles are not adjacent, then they are vertical angles. ________________________
___________________________________________________________________________
4. If a polygon is convex, has five sides, is both equilateral and equiangular, then the
polygon is a regular polygon. __________________________________________________
__________________________________________________________________________
Geometry A
2
Ms. Busskohl
Good luck to: _________________________________
Date: ______________________
V. Complete the proofs. (10)
1. 6( x  4)  60
_______________________
Original Equation (Given)
_____________________________________
_______________________
______________________________________
________________________
_______________________________________
2.
1
  x  8  45
4
Original Equation (Given)
__________________________
_________________________________________
__________________________
__________________________________________
__________________________
__________________________________________
3. Given:
AB  FG
A
AC  EG
10
G
E F
Prove: EF = 3
Statement
B 3C
Reason
1. AC = 13, BC = 3
________________________________________
2. AC = AB + BC
_________________________________________
3. 13 = AB + 3
__________________________________________
4. AB = 10
__________________________________________
5. AB  FG, AC  EG
__________________________________________
6. AB = FG, AC = EG
__________________________________________
7. EG = EF + FG
__________________________________________
8. 13 = EF +10
__________________________________________
9. EF = 3
__________________________________________
Geometry A
3
Ms. Busskohl
Good luck to: _________________________________
Date: ______________________
A
4. Given: ABC is a right angle
BC is an angle bisector.
D
Prove: m DBC  450
B
C
Statement
Reason
1.
ABC is a right angle
__________________________________________
2.
ABC  900
__________________________________________
3. BC is an angle bisector.
90
4. m DBC 
2
0
5. m DBC  450
5. Given:
Prove:
__________________________________________
__________________________________________
__________________________________________
1 2
4
3 4
Statement
1
3
2
Reason
1. ____________________________
_________________________________________
2. ____________________________
_________________________________________
3. ____________________________
_________________________________________
4. ____________________________
_________________________________________
Geometry A
4
Ms. Busskohl