advanced geometry unit 2 intro to logic & proofs

Advanced GeometryUnit 2

Intro to Logic & Proofs

PRIZE SHOW

3. 2.

4.

7.

10.

5.

8.

11.

6.

9.

12.

1.

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 .

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.

3. Always, Sometimes or Never?

Sometimes

b. Vertical angles are supplementary.

Always

a. The supplement of the complement

of an angle is obtuse.

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 .

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

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.

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:

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

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 .

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 .)

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 .