PRIZE SHOW
Advanced Geometry
Unit 2
Intro to Logic & Proofs
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
1. Always, Sometimes or Never?
a. The supplement of an obtuse 
Always
is acute.
b. If 2 's are  to 2 complementary
's, then they are  .
Sometimes
c. If 2 's are complementary to
2  's, then they are  .
Always
2. Always, Sometimes or Never?
a. Supplementary  ' s are  .
Sometimes
b. The complement of an angle
is congruent to its supplement.
Never
3. Always, Sometimes or Never?
a.The supplement of the complement
of an angle is obtuse.
Always
b. Vertical angles are supplementary.
Sometimes
4. Always, Sometimes or Never?
a. The contrapositive of a conditional
statement is reversable.
Sometimes
b. The converse of a definition is true.
Always
c. Two 's supplementary to
Always
the same  are  .
5. Always, Sometimes or Never?
a. If BE bisects ABD, and
BF bisects DBC, then
EBF is a right angle. A
E
D
F
B
C
Always
b. If line a  line b and line b  line c ,
then line a  line c.
Never
6. Given: "If it doesn't rain, the Tigers will win."
a. State the converse.
If the Tigers win, it won't rain.
b. State the Inverse.
If it rains, the tigers won't win.
c.
State the Contrapositive.
If the tigers don't win, it rains.
7. The measure of the supplement
of an angle is 6 more than 7 times
the complement of the angle. Find
the complement.
Complement = 14°
8. Given: "If ABC = 105, then ABC is not acute."
a. State the converse.
If ABC is not acute, then ABC = 105.
b. Is the inverse true or false?
False.
c. Identify a counterexample:
Sample answer:
ABC = 100.
9. Complete the Truth Table:
r p  q 
p
q
r
r
q
T
T
T
F
T
T
T
T
F
T
T
T
T
F
T
F
F
F
T
F
F
T
T
T
r
10.a. Given: AD  DG;
If B and C trisect AD, and
F and E trisect DG, by what
property does AB = FE?
I
B
A
H
1
Segment Division Property G
(Like divisions of  segments are  .)
10.b. Why is 1  5 ?
Vertical 's are  .
3 C
4
E
2
F
D
5
J
I
11. If AD  DG and
BD  GE, by what property
is AB = ED?
B
A
H
1
3 C
4
E
2
F
D
5
G
Segment Subtraction Property
(If  segments subtracted from  segments,
then their differences are  .)
J
12a. Why is 1 supp. 2?
I
A linear pair is supp. (Two adjacent angles
forming a staight angle are supp.) A
12b. If 1  3,
why is 2  4?
Supplements of  's are  .
H
1
G
12c. If 1  5, and 5  3,
why is 1  3?
Transitive property of  .
B
3 C
4
E
2
F
D
5
J