Nal'nÿ ÿ/ÿ l/d-. o

MDLDate

Fill in Notes 1,1

Period

Notes 1.1- Points, Lines, & Planes

Quadrant II Quadrant ; Ordered Pair: (x, y)

x=coordinate:

Quadrant III Quadrant IVy-coordfnate:

X/ÿJ, LIÿfJÿ,r [/[1)ÿ/.f'!!) -points that ÿ__ on the ,Jt/!ÿlt, ].,,i!lÿ.,[

Picture:

- points that tÿl(l .ÿII{, l/lil on the ÿIVÿ/I, J /

AI' it takes is for [)ÿIO point/ within the set of points to be/ .

/ ÿ the line to be consideredNfl; K,

Picture: ÿ (ÿ,/

,14ÿf'''11ÿ

E× 1:lie on the line,

Find the coordinates of three points that lie on the graph of y = 3x+5 and one point that doesn't

, d

-5 :< riÿ 1,LI, }

JL5

EX 2: Do points R(4, 8) and S(-3, -7) lie on the line with the equation y = 2x - 1?

Guided Practice:1, Write the ordered pair for points

T

u 1

i

.... ÿ4m', .... L.ÿ., , • 4-° ...... ' ....... ',1 , ÿ'

t'-, d i ÿ: I 13 I Iÿ 1 ,

i

.... ' ...... =} ............... E1'',- ÿ" ". ........ 4ÿ,

1

f

2, Which quadrant is point C located in? point D? ....

3, Does the point(2,5) lie on the graph of y = 3x+67 I\lU

5 = Iÿ f-bÿk-lm '/, kid<"

4, Does the point (-4, -6) lie on the graph of y = 3x + 6?

{!ÿ ,:: ><,+ {ÿ,• -- Irÿ ...... IZ +,/,ÿ,ÿ

Vocabulary:

Undefined Terms - no formal

- an

by a

Written as:

picture:

°A

- collection of

extending directions,

Written as:Picture:

/./

//1

in all directions.

Written as:Picture:

- Points that in the

Picture:

ll it takes is forÿ pointÿÿwithin the set of points to be ÿ xÿ

e plane to be considered /

Defined Terms- terms that can be t/]ÿ,, ,

such as p ÿ)!iÿ or

- part of a lineL

al, _ÿ4/ÿ/ÿiÿ , on the line the endpoints,

and

Picture:

J

Written as:

-part of a line with ÿ endpoint that ,[4Xÿ[//¢ÿ ÿ

T be written as ÿ._@ÿ Theÿÿ

is always the first letter 'ÿ

the notation for a ray, The )he ray is pointing Is always /

.ÿ2nÿ letter written'

Picture:

If point C lies on A--Bbetween A & B, then C-A'and C-B"are opposite rays.

Picture:

at exactly

point,

Picture:

ii " • ........... ÿ...... ..... '-bI

u9

, __- two lines that

0

Line AB is perpendicular to line CD

Picture:

7

,o,.,,o. for PIlÿYbtÿ(ÿ£I

Line AB is parallel to line Cb

- two lines that,

Picture:

intersect, .,Fj fÿ!l tj,ÿl ÿ,

4

Pictur______£: ÿ_ÿ ÿ..ÿ ÿ.,

Line m intersects line k at point F

and a intersect at a

Line k intersects plane A at point B

planes intersect at a

Picture:ÿ,ÿ

° I

Plane M and plane C intersect at line AB

EXAMPLE: FinishJ

the sketch.

line in the plane line not in the plane

III

line intersects at one Dÿint1

NamÿMDL

Date, Period

Fill in Notes 1.2

Notes 1.2 - Segments & Congruence

The length of a segment is ÿhÿI OÿA ÿ ÿ between its IÿAIÿ)

Draw an example of a point that would be between A and C,

The measure of AB is written as

Zt iS the 0!ÿk5 ÿ (ÿ i bÿtween i ÿ and ÿ i' So the measure of a ,,.<ÿ,#ÿ/!,,#ÿJA ifÿ i ÿ

its two endpoints.

Is the distance from A to B different than the distance from B to A?

....

\!lÿ ,, ÿ,, Why or why not?

A postulate is a

The Ruler Postulate:

The numbers on a ruler are a

between twopointsonanumberlineisthe ÿ(!lÿt'I/ ÿI/ÿlÿ/ÿI.,/

of the difference of the coordinates. It can be found using:

41 ¢ ÿ, ÿ AB: zÿ° I

EX 1:x

< I I I-+-f-, ,ÿ-q-,, I I I I I I i I ,ÿ-+-f-ÿ-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

EX____Z2: Find PQ, QR, and PR if P is located at -3, Q is located at 1, and R is located at 6,

Y-=ll--ÿl=1-ÿ1==5 ÿ 9"

Seqment Addition Postulate: If Q is

P and R.

P q

F----PQ I Qÿ

small segment + small se.xjmÿnt = big scgnlÿnt

EX 3: Find LM if L is between N and M, NL = 6x- 5, LM = 2x + 3, and NM = 30,

I'4IJÿ-LIÿ4, ÿ t',t ÿA 5-> xÿ q-

y,]

• 7;,(ÿ 7y, :ÿ,}7ÿo, .... ÿ-ff;771E×___44: Find the measure of MN if N is between M and P, MN = 3× + ÿ7 and MP = 5x,

lÿi,l+klP':Mr> /> 'tO 7.)t i,ltl,.I-O(/d)-i 7.g # "@ Iÿft., ¢1

'I " ......... 1 r'*ti'l : %2'ÿj-p <-at----------- 'ÿ'1,-t.. 70 :J.!)X. " ..... -ÿ-

Coÿ_.ÿrLleflceÿ

Congruent means .__ÿ#i) ÿ-'I} and is written as

Co2D_g_ruent semi_s- segments that have the

S,\

congruency marks

Lengths are equal,

Aÿ -- (.,[.ÿ:>"iÿ equal to"

Segments are congruent,

"is congruent to"

EXÿ: Use the picture below to find AB if K is between A and B, AK = 2x + 10 and KB = 5x + 4,

A KX t- I0

B

,ÿ/n)//ÿ: y//<'>

/ÿ-B- IV- ÷/V- --- 2ÿ .< .......... __ .......... .,ÿ

Name Iv,ÿ Date PeriodMDL(] Fill in Notes 1.3

Notes 1.3 - Midpoint & Distance FormulasI

*Remember: To find *he ÿ from one endpoint to another ona number line use the iJrÿ]l,ÿr ÿl)ÿÿ,ÿ[/ :,

AB: IX,r)(,I

- the midpoint of a segment is the point thatthe segment into ÿ//) _ congruent[ ÿ )segments.

the midpoint M of PQ is the pointbetween P and Q such that PM : MQ 8

P

Number Line Midpoint Formula:To determine the midpoint on a number line add the two endpointsand divide by 2,

EX 1:X A Y B

<t111 l l l l I I 11111-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

What is the coordinate of the midpoint of AB? -ÿ# ÿ ÿ.

illWhat is the coordinate of the midpoint XY?

means to . in

A bÿ V/ÿ/ff, r/Y,\bt?!O- is a point, rp.v, line, llne segment, or plane thata segment at its ÿ, A midpoint or segment

bisector bisects a segment.

AI]ÿx.'l -: f4ÿ!'> ÿ,,Ad., tlH .- H l;.ÿ,

wEX___22: Line RM bisecÿ LK at point b. Find DK if LK is 16 inches.

\ !IL.-ÿ ........... . ......... o°[

EX 3: U is the midpoint of XY. If XY = ;16x - 6 andUY = 4x + 9, find the value of x and XY.

I{ÿ )t-b

7, ÿ,<q bt,, ÿtx+'] \/

Xu, t+//ÿ,/=X'7h<t t <1j, ÿ ty, P} ÿ-ÿ' IIo X-{,:

'77= 7;,:*"7 X

+,

)t\/=

EX 4: If P is the midpoint of Cb and PC = x and PD = 5x - 4,find the value of x and the measure of CD.

c x F ÿX.Ur p

= FP

P6- P ÿ 76= 77, :: D7 ÿ LI Pc., :: I

Pl):: I..... q>::-"-I o

o o ÿ,p=14-1

CoÿCÿoJardinate plane midpoint formula:

The coordinates of the of a segment whoseendpoints are (xl, yl) and (x2, yz) are

EX___55: The endpoints of RS are R(I, -3) and S(4, 2). Find the midpoint.

EX 6; The midpoint of RQ in the graph below is P(4, -1),

Find the( 0)c°°rdinates of R if Q is at (3,-2)rÿiÿll ÿ ÿÿ ÿbÿ ÿ ÿ ÿ1 ÿ ÿ ÿ. Jm{ÿlÿ--]ÿ'ÿ&0 { I;

I2L'T !-":

}ÿi-ÿ--ÿ v-.i-4.-q," 4...,-

-TI , ÿ ' ' T-'z

-ÿ-+-, I ....... >4-,,-1

7:;. ÿ2ÿ T L 5<ÿb(ÿ,bh,ÿcÿcu

EX 7 What happens when you are missing an endpoint?)ÿlfÿ Iÿjÿ t)lÿIIÿIÿ #The midpoint of JK is M(2, 1). One endpoint is J(1, 4). ()Find the coordinates of endpoint K.

,ÿ

t

Co_oral)hate Plane Distance For u_m_uÿla:

The ÿ between 1-wo points (xl, Y0 and (xz, yz) on a coordinateplane can be found using the JÿfSÿTxÿ4 ÿ, ÿÿ.

d Uÿ Z

EX 8: Find the length of RS if R(1, -3) and S(4, 2),

TiLt: : iiiÿ ÿ: i ÿ::i:ÿiÿ"z "]Fÿ,,,;t .ÿ r-lZ.

V ,2 r" 0

...... L.!/ÿs:ÿ

t lEX £: Determine if the two segments A B and L-K are congruent,

AB: A(4, 6), B(7, 2) LK: L(-1,-6), K(4,-6)

LIL

baleFill in Notes 1.4

Period

Notes 1.4 - Measure & Classify Angles

directions along the same line.are rays that share an ÿ/ÿ(I,pÿltÿ,l and extend inÿ!Iÿ /

H

AnlKÿisformedby 2ÿ with aÿendpoint,

B

BA and BC are fheÿ. of the angle. /B is the common endpoint called theÿ

C

Name angles with three letters

C

bP

Angles are measured in

Aÿcan be used to find the measure of an angle.

Addition Postulate:

Ps

If P is the interior of < RST, then

EX 1: Given that m< LKhÿ 145°, find m< LKÿ and m< MKN.

÷ lo)o IN

(4× - 3)°

K M

ivi ÿ- Llÿtÿl-i vvÿ z ÿIF.M :, tvÿ ,ÿ I.VM

X; 7..ÿ;

tv,,,, Ltrÿ : 7/,7,:ÿ)t !0/77to,>

Classffÿg Ang_/ÿ

AJ .ÿ

fÿ,')I-, qO" '70<ÿt' >'l,1 ÿ- f,,77

EX 3: Given that <KLM is a straight angle, find m< KLN and m< NLM,

M

,

--IDo-_ÿ

.,-ÿ rFT.--l- 71

ivv.ÿ,lf-ul --: rjÿ7.:::=..__

EX 4: Given that < EFG is a right angle, find m< EFH and m< HFG,

8%-77Xÿ fi°/

E;

(2× +2)ÿ/

6

Yÿ Zr H F(ÿtÿ ÿq "t" I

iÿz!7:F 1tÿ t(11")ÿ 7 oÿ --#10-ÿ0W - t:O°

d' ,9.1-GD ÿ qO'',,'

,.:( ,y,,-angles that have theÿmeasure,How would you mork theangles 1o show congruency?

m< ABC : m< A FG"iS ÿqUol to"

,,' ., oj:aO, oAÿls a ray that divides an angle into tw ] nglÿ.

/ -Congr, uÿncy markÿ ÿ BC bisects < ABDfor o.glÿÿÿÿ'ÿ < A BC N= < CBD

B ÿ-.-._.zÿ

b_._..J

LOktt-,/ÿ z tXtÿ-I"x-ÿt lo -5X-16

b X A

DateFill in Notes 1.5

Period

Notes 1.5 - Anqle Pair Relationships

**Re_ÿ:

Intersectinÿ - two lines that meet at exactly one point.

Perpendicular ÿ ( _L. ) - two lines that intersect to form 900 angles,

Parallel lines ( // ) - two lines that NEVER intersect.

S

I ,

,ÿ1t!ÿ,. V . Z-cÿ - two angles whose sum is 90o

'*angles can be named with one letter or number. You

IÿDC__ÿ.must use three #etters when clnglÿ ore Odjfltent alld_ there IS nO number.

Must use 3 letters fÿr this pro.lure

H

,K ÿ

U

OR

zÿ

> ,-A 5(., + ÿ4 L e/13I>--/ÿ0°

--.,,

- ?wo angles whose sum is 180°R

OR

Find the measure of the complement and the supplement of <1.m< .!. = 22o

Xÿ_Z: < i and < 2 are complementary angles and <2 and < 3 are supplementary angles.Given the measures of < 1. Find m< 2 and m< 3,

m< 1 = 36o

m<2= ÿL[lÿ-I +msg =qO°

z ;if-, yq"EX_.__!: < A and < B are complementary angles, Find the measure of each

angle if m< A = (Tx + 21)o and m< B = (9x + 5)°,

>4-1,m,9.-- q0

I(0>l¢t4: '16qf-ÿ qd #

.EX 4.: < A and < B are supplementary angles, Find the measure of eachangle if m< A = (7x + 21)0 and m< g : (9x + 5)°,

Iÿ,!t-ÿ qÿ-/,r,s 110

I{ÿX ÿ IÿI' 22 HI"re<A= re<B=

Two adjacent angles are aÿ if theirÿare oppositerays, The angles in a linear palr &e anglea, Remember palrmeans two!!!!

j

JML and < LMK are a linear pair < PQR and < RQT are a linear pair< PQS and < PQR are a linear pair< RQT and <TQS are a linear pair< TQ5 and ÿ PQ5 are a linear pair

< I and < 3 are vertical angles

< 2 and < 4 are vertical angles

***Vertical angles are always_ÿ_.ÿ!!!%1

EX 5: < FGH and < HG3 form a linear pair, Find the measures ofthe angles if m< FGH = (12x ÷ 1)° and m< HGJ = (4x -9)0

4; 11 ,ÿg

............ f

EX 6: ÿ-ÿand ÿ intersect at point E, Find the measure of<AEC and < CEB if m< AEC : (12x - 5)ÿ and mÿ BED = (4x + 19 °*Hint* Draw a picturetl

.. !tÿ, g ÿ,:,, ÿ-1 x.ÿl., i,;1

lÿ/ÿ

There are some things you can conclude from a diagram and some you cannot conclude,

,

C

Can Concludÿ

° L iÿ iv, I4ÿ,ÿ ÿ'ÿ

Cannot Conclude

,dc,

MI>LPeriod

Fill in Notes 1,6

Noÿes 1.6 - Classify Polygons

A !ÿ0!tAf;ÿYbis a closed figure formed by a finite number of-/ \ ÿ ÿ" ,'o '

segments calledÿwhere each s de intersects exactlytwo other sides at their endpoints.

Each endpoint of.a side is aÿof the polygon

- no line that contains a side of thea point in the interior of the polygon.

conwx po lygo n

/ ÿ( l V ÿ / j;ÿ)lÿ'ÿ{)ÿ]ÿ(ÿ ÿ p 0 ÿ y ÿ 0ÿ that is not convex, Also callednonconvex. 0 (]'I)

concave polygon

EX!: Tell whether the figure is a polygon, If it is a polygon, tellwhether it is concave or convex,

I'

\

/

!

' all interior ang

and Iÿlÿ(ÿl@kt/IV coNvEx polygon,0 J

EX2z How would you mark the following polygons to show that they are regular?

Regular Pentagon

0Regular Hexagon

# of :{Ides

3

4

5

6

7

B

9

I0

2

Typÿ of polygon

@ikti, O4%rÿ.

Classifying polygons

EX 3: Classify the polygon by the number of sides, Tell whether theupolygon is equilateral, equiangular, or regular, Explain your reasoning,

i

EX 4: Draw a figure that fitsVrhe description.

A pentagon that is equilateralbut not equiangular. ÿ'-ÿ

A concave heptagon

The length(in meters) of two sides of aÿar pentagon arerepresented by the expressions 7×- 8 anÿ 10,Find the length of a side of the pentagon,

Sxÿlÿq-;ÿ 4-1D

l@lol-l f l#

EX____66: Find the value of x of the regular polygon,

- Xt -Xÿ

Tx-/o: Ltxÿ-7,ÿ

r I{

+ 4X + 22)°