Name: __________________________
Block: ______
Date: _________
Use the following conditional statement:
If you like to dance, then you go to the BRHS homecoming.
1.) What is the hypothesis?
2.) What is the conclusion?
3.) Write the following in words and symbols. Then determine if the statement is true or false.
(a) converse:
True or False
(c) contrapositive:
(b) inverse:
True or False
(d) biconditional… if possible
True or False
4.) Write the converse of “If M is the midpoint of PQ , then MQ = ½ PQ.”
5.) Provide a counterexample:
If m  3 + m  4 = 180, then  3 and  4 are a linear pair.
Determine if the 3rd statement is a valid conclusion based on the previous two. If it is state
what law was used (Law of Detachment or Law of Syllogism), if not state INVALID.
6.) (1) If points A, B, and C are collinear,
then they all lie on the same line
(2) A, B, and C are collinear.
(3) A, B, and C are on the same line.
7.) (1) If you are published, then
you wrote a good article.
(2) Kendra wrote a good article.
(3) Kendra was published.
Determine if the 3rd statement is a valid conclusion based on the previous two. If it is state
what law was used (Law of Detachment or Law of Syllogism), if not state INVALID.
9.) (1) If John passes the test, then
he passes Geometry
(2) If John passes Geometry,
then he passes 9th grade.
(3) If John passes the test, then
he passes 9th grade.
8.) (1) If you practice your Geometry,
then you will improve
(2) Jenny practices her Geometry.
(3) Jenny’s Geometry grade improves.
Determine the conclusion and state the law used. If not valid, write “invalid.”
10.)
All guinea pigs have four legs
Squirt is a guinea pig
11.) If Kim lives in Loudoun, then Kim is in VA.
12.)
If Sue goes to the market, then she buys eggs.
Sue bought eggs.
If Kim is in VA, then Kim lives in the U.S.
_____13.) Which of the following could you refer to as the reason for a statement in a proof?
A postulate
B definition
C given
D any of these
_____14.) Choose the statement that follows from the statements below:
(1) If M is the midpoint of AB , then AM = MB.
(2) If AM = MB, then AM  MB
A AM = MB
C If AM = MB, then AM  MB
B If M is the midpoint of AB , then AM  MB
D If M is the midpoint of AB , then AM = MB.
_____15.) According to the Venn Diagram, which statement is true?
A All parallelograms are squares.
B Some parallelograms are trapezoids.
C All squares are parallelograms.
D No parallelograms are squares.
Parallelograms
Squares
Trapezoid
s
______ 16. If the conditional statement “If you eat a salad, then you eat vegetables” is
represented by p→q, what is the symbolic representation of
“If you eat a salad, then you don’t eat vegetables”?
A q → ~p
B p → ~q
17.) Given: -2(3x – 4) = 3x + 12
C ~q → p
Statements
D ~q → ~p
Reasons
Prove: x =-4/9
Name the prop. of equality, definition, postulate, or Theorem that justifies each statement.
18.) If EF = GH, then EF – CF = GH – CF.
19.) If S is the midpoint of Q and T,
then QS = ST.
20.) m  B = m  B
21.) If  2 is complementary to  4, then
m  2 + m  4= 90.
22.) If BE bisects  DBF, then
m  DBE = m  EBD.
23.) If  3 and  2 are vertical angles, then
 3  2.
Use the diagram to determine whether the statement is true or false. #22-28
U
24.) Points R, S and T are collinear.
R
25.)  UTR and  UTW are supplementary.
T
S
26.) Points R, S, and T lie in the same plane.
V
X
W
27.) TS is perpendicular to RS .
28.)  VTS and  UTX are vertical angles.
29.)  STR and  RTU are complementary.
30.)
RW bisects  UTS.
Match the appropriate definition, postulate, or theorem with the statement. #29-38
A.
B.
C.
D.
E.
F.
G.
Segment Addition Postulate
Angle Addition Postulate
Definition of Midpoint
Definition of Segment Bisector
Definition of Angle Bisector
Vertical Angles Theorem
Definition of complementary Angles
H.
I.
J.
K.
L.
M.
N.
Definition of Perpendicular Lines
Definition of Supplementary Angles
Congruent Supplement Theorem
Congruent Complement Theorem
Definition of Right Angle
Linear Pair Postulate
Right Angle Congruence Theorem
H
_____31.) If m  1 = 90, then  1 is a right angle.
_____32.) If HE = EI, then E is the midpoint of HI
_____33.) If GE  DF , then  1 is a right angle.
D
_____34.) If  2 is supplementary to  3 and  FEI is
supplementary to  3, then  2   FEI.
2
3
1 E
6
_____35.) m  4 + m  5 = m  FEI
_____36.) If EG bisects DF , then E is the midpoint of DF .
_____37.) m  DEI +  IEF = 180
_____38.) If EJ bisects  FEI, then  4   5.
_____39.)  3   DEI
_____40.) If m  6 + m  FEI = 90, then  6 and  FEI are complementary.
F
4
5
J
I
G
Proofs. Fill in the blanks.
41.) Given: AB  CD and CD  EF
Prove: AB  EF
Statements
Reasons
1.
1.
2. AB = CD and CD = EF
2.
3.
3. Transitive Property of Equality
4. AB  EF
4.
42.) Given: ABC  DEF , BM bisects ABC , EN bisects DEF
Prove: ABM  DEN
A
M
Statements
Reasons
1. ABC  DEF
BM bisects ABC
EN bisects DEF
1. Given
2. m  ABC = m  DEF
2. Definition of Congruent Angles
3. m  ABM = m  MBC
3. Definition of  bisector
4. m  DEN = m  NEF
4. Definition of  bisector
5. m  ABM + m  MBC = m  ABC
m  DEN + m  NEF = m  DEF
5. Angle Addition Postulate
B
C
N
D
6. m  ABM + m  MBC = m  DEN + m  NEF 6. Substitution Property of =
7. m  ABM + m  ABM = m  DEN + m  DEN 7. Substitution Property of =
8. 2(m  ABM) = 2( m  DEN)
8. Substitution Property of = (x + x = 2x)
9. m  ABM = m  DEN
9. Division Property of Equality
10. ABM  DEN
10. Definition of Congruent Angles
F
E