An is right its measure is 90º.

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10 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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DEFINITIONS, POSTULATES, AND THEOREMS

A definition uses known words to describe a new word. Point, Line, and Plane must be commonly
understood without being defined.

Undefined terms
:

Point
-

understood to be a dot that represents a location in a plane
or in space.

Line
-
understood to be straight, contains infinitely many points, extends infinitely in 2 directions, and has
no thickness


Plane
-
understood to be a flat surface that extends infinitely in all directions.


1)

Definition


tells meaning of term. De
finitions are always biconditional.

2)

Postulate



rules that are accepted as being true

3)

Theorems



rules which must be proven true.

4)

Points Postulate
-

a line contains at least 2 points; a plane contains at least 3 non
-
collinear points; space
contains at least

4 non
-
collinear, non
-
coplanar points.

5)

Line Postulate
-

2 points are contained in one and only one line.

6)

Plane Postulate
-

3 non
-
collinear points are contained in one and only one plane.

7)

Flat Plane Postulate
-

If 2 points are contained in a plane, then the

line through them is contained in the
same plane.

8)

Plane Intersection Postulate
-

If 2 planes intersect, then they intersect at a line.

9)

Congruent
-

same size and shape

10)

Similar
-

same shape

does not have to be same size

11)

Segment

(def)
-

a straight path from one
point to another.

12)

Ray

(def)
-

an endless straight path from a starting point.

13)

Opposite Rays

(def)
-

2 rays that share a common endpoint to form a line.

14)

Space (
def)
-

the set of all points.

15)

Collinear Points

(def)
-

points that are contained in one line.

16)

Non
-
col
linear Points

(def)
-

points NOT contained in the same line.

17)

Coplanar Points

(def)
-

points that are contained in the same plane.

18)

Non
-
coplanar Points

(def)
-

points NOT contained in the same plane.

19)

Coplanar Lines

(def)
-

lines that are contained in the same pl
ane.

20)

Non
-
coplanar Lines

(def)
-

lines NOT contained in the same plane.

21)

Angle

(def)
-

is the union of two non
-
collinear rays which have the same endpoint.

22)

Interior of an Angle

(def)
-

inside of the angle

23)

Exterior of an Angle

(def)
-

outside of the angle.

24)

Right

Angle
(def)
-


An

is right


its measure is 90º.

25)

Acute

Angle
(def)
-

Acute angle < 90

26)


Obtuse

Angle
(def)
-


Obtuse angle > 90


27)


Straight Angles

(def)
-

Straight angle = 180.

28)

Segment Addition Postulate



I
f point P is between points A and B, then AP + PB = AB.

Sum of parts
equal whole.

29)

Angle Addition Postulate
-

If B is in the interior of <APC, then m<APB + m<BPC = m< APC. Sum of
parts equal whole.

30)

Adjacent Angles

(def)
-

two coplanar angles with a common sid
e and no common interior points.

31)

Intersecting Lines

(def)
-

are coplanar and have exactly one point in common. If intersecting lines do
not meet at right <s they are oblique.

32)

Parallel Lines

(def)
-

are lines that are coplanar and do not intersect. (same sl
ope)

33)

Skew lines

(def)
-

two lines that do not lie in the same plane. Noncoplanar lines that do not intersect.

34)

Perpendicular Lines

(def)
-

lines that intersect to form a right angle. (negative reciprocal slopes)


2 lines

they form 90º
’s.

35)

Midpoint of a Segment

(def)
-

A point is a midpoint

it divides a segment into 2

segments.

36)

Bisector of a Segment

(def)
-

is a set of points whose intersection with the segment is the midpoint of
the segment.

37)

Perpendicular Bisector of a Segment

(def)
-

A line is a perpendicular bisector

it is perpendicular
to the segment and goes through the seg
ments midpoint.

38)

Angle Bisector

(def)
-


A ray is an

bisector

it divides an

into 2
’s.

39)
Vertical Angles

(def)
-

2
’s are vertical

they are nonadjacent
’s formed by intersecting lines.

40)
Linear Pair of Angles

(def)
-

2
’s are a linear pair
they are adjacent
’s whose noncommon
sides are opposite rays.

41)

Complementary Angles

(def)
-

2
’s. are complementary

their sum is 90º.

42)
Supplementary Angles

(def
)
-

2
’s. are supplementary

their sum is 180º
.

43)
Linear Pair
Theorem
-

If 2
’s that form a linear pair

they are supplementary.

44)
Congruent Supplem
ents Theorem
-

If 2
’s are supplementary to the same
or

's

they are
.

45)
Congruent Complements

Theorem
-

If 2
’s are complementary to the same
or

's

they are
.

46)
Vertical Angles Theorem
-

I
f 2
’s are vertical

they are
.

47)
Def. of congruent angles or segments



If two angles or segments are congruent, then they have equal
measure.

48)

All right
’s are
.

49
)
Congruent Complements Theorem

-

If 2
’s are complementary to the same
or

's

they are
.

50
)
Congruent Supplements Theorem

-

If 2
’s are supplementary to the same
or

's

they are
.

51)
If 2

's are supplementary

they are right
’s.

52)
Common Segments Theorem

-

If 2 segments are formed by a

pair of

segments and a shared
segment

the resulting segments are
.


Properties from Algebra:

Let a, b, and c be real numbers.

Addition Property

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

(add same thing to both sides of an equation)

Subtraction Property

If a = b, then a


c = b


c.

(subtract same thing from both sides of an equation)

Multiplication Property

If a = b, then ac = bc.

(multiply both sides by same thing)

Division Property

I
f
a = b and c = 0, then a / c = b /

c.

(divide both sides by the same thing)

Reflexive Property

For and real number a, a = a.

Symmetric Property

If a = b, then b = a.

Transitive Property

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

Substitution Property

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

Distributive property

If a(b + c), then ab + ac.


Formulas to Know:

Distance Midpoint