Download Conjectures

C-16
Center of Gravity Conjecture The centroid of a Hiangle is Ihe cenler of gravill' of Ih,'
Iriangular region, (Lesson 3,8)
"
Conjectures
Chapter 2
Chapter 4
C·l
Linear Pair Conjecture If two angles form a linear pair. Ihen the measures of Ihe angb
aJJ up 10 180°, (Lesson 2,5)
C·2
Vertical Angles Conjecture If two angles are vertical angles, Ihen Ihe" Jr,' (nnp-rU,'''1
(have equal measures), (Lesson 2.5)
C-17
Triangle Sum Conjecture The sum of Ihe measures of Ihe angles in every "iangle is
180°, (Lesson 4.1)
C-18
Third Angle Conjecture If two angles of one Iriangle are equal in meJ,ure 10 1"'0 angb
of another triangle. then the third angle in each trian~le is equal in Illeasure 10 Ih,' IhirJ
angle in the other triangle. (Lesson 4, I)
C-3a
C-19
Isosceles Triangle Conjecture If a Iriangle is isosceles. then its base angles are congruent.
(Lesson 4.2)
Corresponding Angles Conjecture, or CA Conjecture If two parJlleiline, are (UI hl' J
transversal. Ihen corresponding angles are congruent. (Lesson 2,6)
C-3b
C-20
Converse of the Isosceles Triangle Conjecture If a triangle has IwO congruenl angles,
then il is an isosceles triangle. (Lesson 4,2)
Alternate Interior Angles Conjecture, or AlA Conjecture If two parallel lines are cui I
a Hansversal. then ahernale interior angles are congruent. (Lesson 2,6)
C-3c
C-21
TrilnglelnequaUty Conjecture The sum of the lenglhs of any 11"0 siJes of a IriJllgk is
grealer than the length of lhe third side, (Lesson 4.3)
Alternate Exterior Angles Conjecture, or AEA Conjecture If (WO pJrallei hnes arc Clil
hI' a IrJnSVersal. Ihen ahernate exterior angles are congruent. (Lesson 2,6)
C-3
Parallel Lines Conjecture If Iwo parall,'1 lines are Cui hl' a Iran",ersJI. Ih,'n
C·22
C-23
C-24
C-25
Slde-AnglelnequaUty Conjecture In a Iriallgle, if on,' side i, IOIl~,'r Ih.1l1 allo,h", ,iJ,',
Ihen Ihe angle opposile Ihe longer siJe is IJrger IhJn Ihe Jn~Ic' "1'1""ilc 11ll' ,h"flcf ,ide'.
(Lesson 4.31
SSS Congruence Conjecture If Ihe Ihree sides "I' ou,' Iri.lI1gk
sides of anolher Iriangle. then the Iriallgks Jr,' ((lngrll""!.
,lI,'
,·""~rtll'nl I" Ih,' ,I'f",'
,I.",,", ·1.-11
SAS Congruence Conjecture
'1',,,,,, siJ,'s Jnd Ih,' in,lude'l1 ,lllgl,' '"
congruent to t\Yo sides and the induJl'd
C-27
C-4
JIlg,!l'
of
Jlllllht'r 11"1.1I1~h:. thl'l\
'Ill'
1\\'0
angks anJ.1 IHIU·II1,III.kd ,id,' ", on,' lli,lll~k ,II"
congrUl'n1 10 the corresponding Jngl\'~ ,111..1 >idl,,' 0"
.Uhtlhl'r trl.",~lc. lhell
Ih..., 1ft.111~ll·'
Ijlll':- Jrl'
Perpendicular Bisector Conjecture
:-l·~llll·lll. 111VII II I' 1,:qllidl"·d.1I1[ lrolll
lrl.lll;:h:" .11\'
C-6
(·7
p.H.llkl.
If.1
tllt"
p(lint
I.... IHI lilt' ptTpl'lhlltllJ.ll"
1,: 11 d PtlJlll:--.
Ilt":"Il]}
C-29
Equilateral/Equiangular Triangle Conjecture h,'[I' ,',!uiL'1l"I,tI Ir\.lll"k " "'i'Il,II',,,,L'L
Con\"l~rselr, ~\'ery equiJngular (fiJIl~dl' i) l'quiJ.lIl'f,i1. Ilt':"'I111 .I.~ I
,
(-8
Shortest Distance Conjecture Th . :
Angle Bisector Conjecture II
Irplll
C·g
,h ..:
111\'
10111
,11l;-:k, \11 ,111\
C-l0
,idl''''
Lli
lill' .11I~k'.
,I POlllt j, IIIl
Ilt·...... t)11
Ih...,
Pentagon Sum Conjecture
is 180°(11 - 2). (Lesson 5.1)
I' Ilh· .... llft·d
bi'l'llt'l
III
.111 .11l::k.
1111.:11 i' i.. r.:quidl"I.JI
5.~ I
,11\~k
hi"',I'''' '" ,'lil"",:k ,1\,
C-11
Altitude Concurrency Conjecture
C-12
,,1.1 It 1.111:: It' .lIt·
l
Circumcenter Conjecture
.1 t·".I\) .\.7
nil ... III
"I
J.-:,
'1Ilt' linn' ,1I11111dt"
I Ill'
lilt' llllt· ...... dlll.lllliJl~
1I1l'
It'll (. I I t· ...... t 111 ~.:-.
'Iht' \lldlllht'llh:1 \11 .1 111.111~1,· I' t'ljllhli'l.lI11 1"11111
11\\"
\~·llh.~··
I
Thl' ~llln ,,(llll' 11\t:.I:-url·' of (Ilt' li\~' .111:-:k, 1'1 .111\ Pl'llt.I;:t11l
is 540°, ILesson 5, I )
(·32 Polygon Sum Conjecture The sum of 'Ill' I1ll·J:-.urC'"
lillI.'
II I h.:. ! 1''':''1111 _, ..;,
Perpendicular Bisector Concurrency Conjecture '1 he' ,111"( 1"'11"'1\.1" 1\1.1\ hi,,','I<."
.1 lll.lll!~k .lrt· \1111\ III ft'llL II t' ,...... I 111
qUJJrilaleral is 360°, (Lessol\ 5, I 1
C·31
hl,r.:~·ltlr Ill' .1
.'.~ I
:-hnrh'"'l dhl.Hh.\' Irllm .1 pllllll Itl ,I
Angle Bisector Concurrency Conjecture rh,· Ihr,'"
,1111 [ 11\ I~ ~
Thl' :-WIl \II lilt' Illt·,btLl\' ... III
I'm",
\,.OlhlJll'l·1l1 Illln'l .1\ .1 !'(lilill. (l.t·~~t11l .'.~ I
Chapter 5
(·30 Quadrilateral Sum Conjecture
10'
Converse of the Perpendicular Bisector Conjecture II " 1'''"11 " '·'luid"\.I11\ """'
I ill' l'lhll'PIIU' n(.1 ;-'l·~lIh.'lIl. lIh.'1l it i.. tll1 !III,: j1l,.·!I'l,.'lhhtuLtr hi'l'I[\l1 III I Ill' 'l·~l\\I.·lll.
I Il·.... Pll 3.~ I
congruent. (Lesson 4.5)
Vertex Angle Bisector Conjecture In In i,,,,,d,,, II i,lngk, Ih, hi,,', ,,,' "i 'he' I CI k '
angle is also Ihe ahilUJe anJ Ihc lIleJiJIl '" Ih,' h.I,,,- 11,""'" 4.:';;
H.II,,'w,.t1
{ll""'lill ~.() I
.t1'IIl;': IIh: p(rpl'lh..lilUI., .. ,,,:;':'Ilh.:IH llulll t!I\' 11llilll tl\ till"
.lll·
C·28
,I
Chapter 3
Iri.lI1~k ",,'
ASA Congruence Conjecture If 1\V1I Jngb 'InJ Ih,' illcluJ"d ",k "i ,,,,,' Irr,II1gk ,Ir,'
congruenl to tWo angles and the illl,:luJ\.'d :-.idl' of Jlhllhl'r 1r1.IIlSlt', thl'Jl lih.' lI"i.lIl~k·" .Ilt'
congruent. (Lesson 4.5)
SAA Congruence Conjecture If
.1111.:1"11.1"': . : "h:rill" .1I\~ks, lhl'll Iht'
(-5
'lilt'
2.(l1
Converse of the Parallel lines Conjecture If two li"es arc Clil 1>1'
p.lir, til lOlll:!rlll.:1l1 (nrrt.')ponJlIlg 'lU~ks, \,:ong.rul'llt ahl'rn.llt.' illtL'rior .tI1gk), or . . oll~nh.·111
'x"rlangle Exterior Angle Conjecture The measure of In eXl",ior .Illglc of J Iri'lIlgk i,
equJI to the sum of the nlt"3sures of thl' rt.'I1Wll' inh:ritlf JIt!!h::<o. 11.',::-':-'011 .1..' I
congruent. (Lesson 4.4)
C·26
l,.(lrll,.·:-'ll~llldillg Jllglt':- .lr,,: lOllgrw:ll1. Jlh,:rnJh.' interior .11l~le:-. arl' ,,:ollgnlt'1l1. and .t1ll'rn.lIl'
l'xh,:rin ...tI1gk~ ..H e l·OIl~rth.'lli. {I.,:~~on
1'1
,h\,.·
11 lIlkn,H
.1I1:-:k,
'Iht' ilh:I..'llh:r \11 .1 1II,\II~h.: 1:- (,:qllilli,t,t111 lI'llH !Ill'
C-13
Incenter Conjecture
C-14
Median Concurrency Conjecture
II t· ...... l II I .'.I'!
C-15
Centroid Conjecture
Ill' ,Itl II ;':L111
l11
\,:­
'1 ilt' ... t'lllrnid tl(.\ Ifl.lIl~.dl..· tll\'jlk, c.lth l1lt'dl,lll Illln t\\'o p,lI't-. 'LI
dUI rill' di'l.llht' Iflllll lilt" (t'llirtlid III
lilt' l1lidpllilll
,i"k". clt·, .... 11l
Tilt' Illft't' 11It.:di,llb III ,I IIUll;.:k ,Ill' tlll\lllfl t'lll.
thl'
\lTk\ I.' l\\·itl" lilt' dl'1.1Ikt· 11'0111 (lIt' It'llllllld 1\
tilt' t1PPO:-llt' ~jdl..·. llt':-'tlll .U":l