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Advanced GeometryUnit 2
Intro to Logic & Proofs
PRIZE SHOW
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3. 2.
4.
7.
10.
5.
8.
11.
6.
9.
12.
1.
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1. Always, Sometimes or Never?
Always
Sometimes
Alwaysa. The supplement of an obtuse
is acute.
c. If 2 's are complementary to
2 's, then they are .
b. If 2 's are to 2 complementary
's, then they are .
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2. Always, Sometimes or Never?
Never
Sometimes
a. Supplementary ' are .s a. Supplementary ' are .s
b. The complement of an angle
is congruent to its supplement.
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3. Always, Sometimes or Never?
Sometimes
b. Vertical angles are supplementary.
Always
a. The supplement of the complement
of an angle is obtuse.
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4. Always, Sometimes or Never?
Always
b. The converse of a definition is true.
Sometimes
a. The contrapositive of a conditional
statement is reversable.
Always
c. Two 's supplementary to
the same are .
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Always
a. If bisects ABD, and
bisects DBC, then
EBF is a right angle.
BE
BF
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5. Always, Sometimes or Never?
A
F
DE
CB
b. If line a line b and line b line c ,
then line a line c.
Never
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a. State the converse.
If the Tigers win, it won't rain.
6. Given: "If it doesn't rain, the Tigers will win."
b. State the Inverse.
If it rains, the tigers won't win.
c. State the Contrapositive. If the tigers don't win, it rains.
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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°
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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 .
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9. Complete the Truth Table:
F
T
FF
F
F
T
T
T
TT
T
T
T
T
T
T
T
T
F
T
F
F
T
q r p q r rqp r
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A B C D
F
G J
EH
I
12
5
34
10.a. Given: DG;
If B and C trisect , and
F and E trisect , by what
property does AB = FE?
AD
AD
DG
Segment Division Property
(Like divisions of segments are .)
10.b. Why is 1 5 ?
Vertical 's are .
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A B C D
F
G J
EH
I
12
5
34
11. If DG and
BD GE, by what property
is AB = ED?
AD
Segment Subtraction Property
(If segments subtracted from segments,
then their differences are .)
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A B C D
F
G J
EH
I
12
5
34
12a. Why is 1 supp. 2? A linear pair is supp. (Two adjacent angles
forming a staight angle are supp.)
12b. If 1 3,
why is 2 4?
Supplements of 's are .
12c. If 1 5, and 5 3,
why is 1 3?
Transitive property of .