a location. A point has no legnth, with, or thickness

A dot and a capital letter

An infinante set of ponts the extends in two directions. Has legnth but no width or thickness.

italic lower case letter

Atleast two point on the line

Infinite set of points that creates a flat surface without ending. Has length and width but no thickness.

italic capital letter

Atleast 3 points in a line

Set of points in both figures. dashes represnt parts hidden from view.

Two lines intersect in one point

Two planes intersect in one line

Named by giving its enpoint and another point on the ray.

Endpoint is named first

Order matters

Distance betweem two pints

distcance= positive

Us absolute value to find the distance.

The points on a line can be paired with the real numbers in such a wat that anyt woto paints can have coordinates 0 and 1.

Take a line segments; put it on a number line then

use the number linw ro measure the distance.

If B is between A and C then AB + BC = AC

If BX is the bisector of <ABC,

then <ABC = 1/2 m<ABC and m<XBC = 1/2 m<ABC

Transitive Property

"three parts"

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

If m<1=m<2 and then m<2=m<4,

then m<1 = m<4

If AB=EF and EF=HS, then AB=HS

(add congruent sign over every = sign,

& add line over every set of letters) 

If AB = DE, then DE = AB

If XY = QP, then QP = XY

(add congruent signs and lines over XY & QP)

A number (or value) will equal (or be = to) itself

PE = PE

m<1=m<1

AB = AB

(add congreunt sign & line of over AB)

<11 = <11 (add congruent sign)

If a=b then either may be substituted for the other

X=3, XTY=17, then 3TY=17  

If a=b, then ca=cb

X=29 then 2x=58

If a=b, then c does not = o, then a/c=b/c

If 2X=200, then X=100

Statement

1.  M is midpoint of AB

2.  AM=MB

3.  AM + MB = AB

4.  MB + MB = AB (2 MB=AB)

5.  MB = 1/2 AB

6. AM=1/2 AB

Reasons

1.  Given

2.  Definition of Midpoint

3. Segment of Addition

4. Substitution

5. Division

6.  Substitions

Right

Given <1+<2 are vertical angles,

Prove <1 =<2 (add congruent sign)

Statements

1.  MC1 + ML3 = 180; M<2 + M<3 = 18

2.  M<1+ M<3=M<27 -- M<3

3. M<3=M<3

4. M<1 = M<2

<11=<2 (add congruent sign)

If AB=DE, then DE=AB

If XY = QP, then QP = XY

(add line over letters & congruent sign)

2 angles such that the sides of one angle are opposite rays to the sides of the other angle. 

They will share a vertex.  Where two lines intersect, they will form 2 pairs of vertical angles.

Complement of LA=90-X

Supplement <A=180X

Given L1 & L2 are supplements

<3+<4 are supplements

<2=<4 (use congruent sign)

Prove < = <3 (use congruent sign)

Statements

1.  See given

2.  M<1 +M<2=180

M<3 + M<4 = 180

3.  M<1+M<2=M<3 + M<4

4.  M<1=M<3

<1=<3 (use congruent sign)

Reasons

1.  See given

2.  Def. Supp. Angles

3. Substitution

4. Subtraction 

If a point Y lies on the interior of <XOZ,

then M<XOY + M<YOZ = M<XOZ

Part + Part = the Whole Postulate

Are copllainear angles with a common vertex,

but NO common interior points

If M is the midpoint of AB,

then AM = 1/2 AB and MB + 1/2 AB

Two lines that intersect to form 4 right angles.

Definition:

1.  If 1+N then each of the angles is 90

2. If 1 of the four angles is 90, thein L-N

"Three Parts"

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

If M<1=M<2 and M<2 = M<4,

then M<1 + M<4

If AB = EF and EF = HS, then AB = HS

(Use congruent sign and lines over letters) 

Statements

1. 3X+6-1/2X

Reasons

1. Given

2. Multiplication

3. ______