Unit 2 pt 1 Flashcards
conditional statement
a type of logical statement that has 2 parts, a hypothesis and a conclusion
If= ______________, then = _________________
hypothesis, conclusion
Counterexample
an example that shows a conjecture is false
(a single example that shows a general conditional statement to be false)
converse
the statement formed by switching the hypothesis and the conclusion of a conditional statement
EX: Conditional - If you live in South Brunswick, then you live in New Jersey. (T)
FIND CONVERSE
If you live in NJ, then you live in SB. (F)
EX: Conditional - If you are a native New Jersey, then you were born in New Jersey. (T)
FIND CONVERSE
If you were born in NJ, you are a native New Jersyan. (T)
BiConditional
a segment that contains the phrase “if and only if”
EX: Conditional statement - If it is Saturday, then I can sleep late.
FIND BICONDITIONAL
If and only if it is a Saturday, I can sleep late.
When will you not have a biconditional?
If the conditional statement and the converse are both true, then you will have a biconditional. Otherwise, you won’t.
p = ?, q= ?
p = Hypothesis, q = conclusion
Reflexive Property
For any real numbers a, a=a
Symmetric property
If a=b, then b=a
Transitive Property
If a = b and b = c, then a = c
Addition Property
If a = b, then a + c = b +c
Subtraction Property
if a = b, then a - c = b - c
Multiplication property
If a = b, then ac = bc
Divison Property
If a = b, and c ≠ 0, then a/c = b/c
Substitution Property
If a = b, then a can be substituted for b in any equation or expression
Theorem
A mathematical statement that must be proven before being accepted
Two-column-proof
Midpoint Theorem
If M is the midpoint of LINE AB, then AM = 1/2 and MB = 1/2 AB
Angle Bisector Theorem
If RAY BX is the bisector of ∠ABC, then m∠ABX = 1/2 m∠ABC and m∠ XBC = 1/2 m∠ ABC
Midpoint definition
The middle point of a line segment
Postulate #1
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.
Postulate #2
Segment Addition Postulate - If B is between A & C, then AB + BC = AC, if Ab + BC = AC, then B is between A & C
Postulate #4
Angle Addition Postulate
If point B lies in the interior of ∠AOC then
m∠AOB + m∠BOC = m∠AOC
Linear pair postulate
If ∠AOC is a straight angle and B is any point not on AC, then
m∠AOB + m∠BOC = 180
Postulate #5
-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
Postulate #6
Through any two points there is exactly one line
Postulate #7
Trough any three points there is at least one (infinite) plane, nd through any three noncollinear points there is exactly one plane (only one).
Postulate #8
If two points are in a plane, then the line that contains the points is in that plane
Postulate #9
If two planes intersect, then their intersection is a line
