Unit 2 pt 1

Question 1

conditional statement

Answer 1

a type of logical statement that has 2 parts, a hypothesis and a conclusion

Question 2

If= ______________, then = _________________

Answer 2

hypothesis, conclusion

Question 3

Counterexample

Answer 3

an example that shows a conjecture is false

(a single example that shows a general conditional statement to be false)

Question 4

converse

Answer 4

the statement formed by switching the hypothesis and the conclusion of a conditional statement

Question 5

EX: Conditional - If you live in South Brunswick, then you live in New Jersey. (T)

FIND CONVERSE

Answer 5

If you live in NJ, then you live in SB. (F)

Question 6

EX: Conditional - If you are a native New Jersey, then you were born in New Jersey. (T)

FIND CONVERSE

Answer 6

If you were born in NJ, you are a native New Jersyan. (T)

Question 7

BiConditional

Answer 7

a segment that contains the phrase “if and only if”

Question 8

EX: Conditional statement - If it is Saturday, then I can sleep late.

FIND BICONDITIONAL

Answer 8

If and only if it is a Saturday, I can sleep late.

Question 9

When will you not have a biconditional?

Answer 9

If the conditional statement and the converse are both true, then you will have a biconditional. Otherwise, you won’t.

Question 10

p = ?, q= ?

Answer 10

p = Hypothesis, q = conclusion

Question 11

Reflexive Property

Answer 11

For any real numbers a, a=a

Question 12

Symmetric property

Answer 12

If a=b, then b=a

Question 13

Transitive Property

Answer 13

If a = b and b = c, then a = c

Question 14

Addition Property

Answer 14

If a = b, then a + c = b +c

Question 15

Subtraction Property

Answer 15

if a = b, then a - c = b - c

Question 16

Multiplication property

Answer 16

If a = b, then ac = bc

Question 17

Divison Property

Answer 17

If a = b, and c ≠ 0, then a/c = b/c

Question 18

Substitution Property

Answer 18

If a = b, then a can be substituted for b in any equation or expression

Question 19

Theorem

Answer 19

A mathematical statement that must be proven before being accepted

Question 20

Two-column-proof

Question 21

Midpoint Theorem

Answer 21

If M is the midpoint of LINE AB, then AM = 1/2 and MB = 1/2 AB

Question 22

Angle Bisector Theorem

Answer 22

If RAY BX is the bisector of ∠ABC, then m∠ABX = 1/2 m∠ABC and m∠ XBC = 1/2 m∠ ABC

Question 23

Midpoint definition

Answer 23

The middle point of a line segment

Question 24

Postulate #1

Answer 24

Ruler Postulate - Points in a line can be matched with 1:1 real numbers. The real number corresponds to a point is the coordinate of the point

The distance between points A & B is written as LINE AB. It is calculated as the absolute value of the difference between the coordinates of A & B. This is called the length of LINE AB

EX:
5 Units
—————————-
<–|—-|—-|—-|—-|—-|—-|—-|—>
1 2 3 4 5 6 7 8

|2-7|=5, this means the line’s length is 5 units long.

Question 25

Postulate #2

Answer 25

Segment Addition Postulate - If B is between A & C, then AB + BC = AC, if Ab + BC = AC, then B is between A & C

Question 26

Postulate #4

Answer 26

Angle Addition Postulate

If point B lies in the interior of ∠AOC then
m∠AOB + m∠BOC = m∠AOC

Question 27

Linear pair postulate

Answer 27

If ∠AOC is a straight angle and B is any point not on AC, then
m∠AOB + m∠BOC = 180

Question 28

Postulate #5

Answer 28

-A line contains at least two points
-A plane contains at least three points not all in one line
-Space contains at least four points not all in one place

Question 29

Postulate #6

Answer 29

Through any two points there is exactly one line

Question 30

Postulate #7

Answer 30

Trough any three points there is at least one (infinite) plane, nd through any three noncollinear points there is exactly one plane (only one).

Question 31

Postulate #8

Answer 31

If two points are in a plane, then the line that contains the points is in that plane

Question 32

Postulate #9

Answer 32

If two planes intersect, then their intersection is a line