Geometry Ch.2

Question 1

Euler Diagram

Answer 1

Question 2

commutative property

Answer 2

a + b = b + a or a ∙ b = b ∙ a

Question 3

associative property

Answer 3

(a + b) + c = a + (b + a) or (a ∙ b) ∙ c = a ∙ (b ∙ a)

Question 4

identity property

Answer 4

a + 0 = a and a ∙ 1 = a

Question 5

inverse property

Answer 5

a + (-a) = 0 and a ∙ 1/a = 1

Question 6

conditional statement

Answer 6

if a, then b

Question 7

hypothesis

Answer 7

if a

Question 8

conclusion

Answer 8

then b

Question 9

contrapositive

Answer 9

if not b, then not a

Question 10

converse

Answer 10

if not a, then not b

Question 11

iff

Answer 11

if and only if

Question 12

definition

Answer 12

when the conditional statement and its converse are true, then it is a definition

Question 13

syllogism

Answer 13

a→b , b→c , c→d so a→d

Question 14

premises

Answer 14

the steps of the syllogism

Question 15

theorem

Answer 15

if all the premises are true and the logic is sound, then the conclusion must be true

Question 16

direct proof

Answer 16

proving all the steps leading from the beginning to the conclusion

Question 17

indirect proof

Answer 17

begins with an assumption that is the opposite of the conclusion, then prove that this assumption is false, so the original conclusion must be true

Question 18

assumption

Answer 18

the idea that is opposite the conclusion and is likely false

Question 19

contradiction

Answer 19

proof that the assumption is false

Question 20

postulate

Answer 20

a statement that is accepted as true without proof

Question 21

postulate #1

Answer 21

two points determine a line

Question 22

postulate #2

Answer 22

three points determine a plane

Question 23

pythagorean theorem

Answer 23

a² + b² = c²

Question 24

Triangle sum theorem

Answer 24

all three angles of a triangle add up to 180°

Question 25

Circumference Theorem

Answer 25

C=πd (circumference = π ∙ diameter)

Question 26

Area of a Circle Theorem

Answer 26

A=πr² (area = π ∙ radias²)