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Section9-1
lntroductionto
Geometry:Points,
Lines,and Planes
Notes
Basic Geometric Fiqures
Vocabularv
Copythe tableon page436
IJ
7',
Example1: Nameeachfigurein the diagram.
a . t h r e e p o i ntsHf , W,K
b. twosegments !q . nT
*--+
,
c. tworays -rK
1-+{
,/
,/
rrTr-
r Twolinesintersect
onepointin common.
if theyhaveexactly
Two linesthat lie in the same planeand do not intersectare parallel.
"isparallel
to."
You usethe symbotll to indicate
o Skew linesare linesthat do not lie in the same plane.They are
Skewsegmentsmustbe partsof
not parallel,andtheydo not intersect.
skew lines.
Example2: Usethe diagramon top of page438. Nameeachof the
following.
ectnr
thatinters
a.foursegments
re , W .W "W
M"w-ft
b. threesegmentsparallelto nP
skewb tr
c. foursegments
Summary:
t[
,m
.-{ b .G
Section9-l
lntroductionto
Geometry:Points,
Lines,and Planes
Notes
Example3: Drawthe figuresindicated.
a. threeparallelsegments
A9
C-
*-
P
--a
eF
of part(a)
the parallelsegments
b. a raythatintersects
-+
- /c
c. a segment ,q,A
f
Summary:
F
e. aline LM
d. a ray QR
a
at
#
Section 9-2
Angle Relationships
and ParallelLines
Notes
Adjacentanglessharea vertexand a sidebut no pointsin theirinteriors.
B1
x.
A
/
zAXB and zBXC are adiacent angles
c
x<
linesandare oppositeeach
Verticalanglesareformedby two intersecting
other.Verticalangleshavethe samemeasure.
T\
2
/
1Xg
4
tL andL3 are verticalsngles
-t-----
z2 and L4 are verttcal angles
-/
angleshavethe samemeasure.
Congruent
Lt = z3 are congruent angles
Youcanwritethe measureof zl asmz1
Since 21, = 23, mz'l- : mL3
An acuteanglemeasureslessthan90
-L
,
90
A rightanglemeasures
t
morethan90 butlessthan180.
Anobtuseanglemeasures
T\
Summary:
Section9-2
AngleRelationships Notes
and ParallelLines
lf the sum of the measuresof two anglesis 90, the anglesare
complementary"
Pt
zPQRand zRQSare complementary
l/zo
o
-{'
,
S
lf the sum of the measuresof two anglesis 180,the anglesare
supplementary,
c/
zABC and zCBD are supplementary
120/
A
B
D
twootherlinesin differentpointsis a transversal.
A linethatintersects
andtwo lineshavespecial
Somepairsof anglesformedby transversals
a
names.
1-\
,/
Z<________
2
Correspondinq anqles lie on the same side of the transversaland in
positions.
corresponding
Alternateinterioranqlesare in the interiorof a pairof linesandon
oppositesidesof the transversal.
t<
/
-:4
"--z#
>
alternateinteriorangles.
anglesandtwo pairsof congruent
corresponding
4-/
ol4trfit tfilfrnvl
L4 anl/.lt
A i l d/ 5
Summary:
(Lnalt
Corw,rrnndno
\
L l h ^ trl { r
L{
/ 4'r,sA
1 7 5*il Llr
I z ^ri,L1
Section9-3
Ctassifying
Potygons
Notes
A potygonis a ctosedfigure with at leastthree sides. The sidesmeet only at
their endpoints.
A triangleis a potygonwith three sides. Youcan classifytrianglesby angte
and sidetength. Tick marksare usedto indicatecongruentsidesof
measures
a figure.
ClassifvinqTrianeles
lsoscetes
triangte
Equitate'rat
triangte
triangle
Scalene
i- ul-' \
Obtusetriangle
Righttriangte
Acutetriangte
eachtriangteby its sidesandangtes.
Example1: Ctassify
O.
a.
l\-
"/
I\./Y
\|
/
frn-rvt
i rade
d
r
..\\
\
'\
lsosrt,l,er
WUNa
Aufu, lytznnq!
obtwEt
I.rwnqV
U
\)
Classifvine Quadrilaterals
Rectangle
Square
four 90 degree
angtes
four 90 degree
angtesandfour
congrtrentsides
Trapezoid
exactlyone pair
of parattelsides
Rhombus
four
congruent
sides
Parallelograrn
both pairsof opposite
- - :l - --- - - - tl - l
par-alrel
5toe5
are
that havefour right angles
Example2: Namethe typesof quadritaterals
A regularpotygonhasall sidescongruentandalt anglescongruent.
Example3:
a. Write a formulato fi4d the perimeterof a regutarhexagon.
b. Usethe formutato find the perimeterif onesideis 16cm.
t!
l(l
4le-an
Section 9-6
Circles
Notes
A circteis the set of pointsin a planethat are the samedistancefrom a given
point, cattedthe centerof the circte.
The ratio of everycircte'scircumferenceC to its diameterd is the same. lt has
"pie." Both3.14and lare good
a specialsymbol,a, whichis pronounced
for this ratio.
approximations
invotvefractions,anduse3.14whenthey do
Use22forzr whencalculations
not.
re-ns-e-sf
eire-umfr
a.qlrcle
The circumferenceof a circteis z timesthe diameter.
o r C= 2 n r
C= nd
of eachcircte.
Example1: Findthe circumference
b.r=200mi
a.d=30mm
5l4
-..---.-ai
I|4Q,r0
wrn
r
x ho
tr
IJOD
-------$-
-- 4ro h,H
A(iiaa)
x 4ln
LS lo.b0 wLt
qrp0
4.?.n Mwl
qt 4
c. d = zlir.
l= =
l4
A x5
5
h,l4
ry t4'' Y
^A,\1s s
TTt
8,8
'
Summary:
w1L
+01
+g
iltn-l
-4{
x-
l25b wr"
'{
d.r=6cm
2llg)=
l'e
6,1+
xla
lr 7&
Ttrt0
qllo 9, hln
bl,lutz.r':t
A centralangteis an angtewhosevertexis the centerof a circle.
A circteis360'.
Example2: Makea circtegraphfor the data provided.
Section9-7
Constructions
Ex"r"p[" fi Drawisegment. Constructa segmentbisectorto the
segmentYoudrew.
E
"rpte
to the tine
segment
a perpendicutar
2: Diiw i tine. Construct
an angtebisectorto the
E arpte 3 Drawanobtuseangte.Construct
angteyou drew.