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Unformatted text preview: Aug 26 08 06:50p FTS ﬂ] QEUI‘EUJ OF Hi5“ SCH‘OOL CEQCL‘DE‘AN> SEOM’ET‘RY HIE" scum crummy Congruehce 1;} ,
' 'mmgles 'Segrnenls Angles . '
EEC—Diff MELBiﬁ AABCEADEFiff
AB=CD mLA=m¢B ABZDE méAszD BC=EF mLB=m¢E
AC=DF mﬁC=mZLF. Basic congruence Criteria C F A a n E
c r
1&3 abs
5' r A 3 D : lgL
. CPCF PRINCIPLE: ASA: If MEAD, 332 SE, and
LB ELE, LhenAABCELD . 538:3E2JTEEED—aand
EElE—Emen AABCEADEF. Corresponding parts of congruent ﬁgures
are congruent. Basic Theorems an ﬁangles ISOCELES TRIANGUE THEOREM: A
HATE Ethan A3 5 LC,
and conversely. MMOR ANGLE INEQUAIM B
If LBCD is an exterior angle of
WC, then mLBCD 1‘: 1114A and mABCD > «1:18. A C D
SCALENE INEQUALITY: C
IfmAA > mLB, than BC>AC.
and conversely. A B
HINGE THEOREM:
[EAR = DE; AC: DFand mLA < mLD . then BC (E17. A A
B C E F
ANGLESUM THEOREM: In any MEG. mm +mLB + mLC=180. A
SlDE—SPLI'ITING THEOREL’I: 0g
B C Hﬁis parallel to then
ADIDB = AEEC. 5125551212 p.1 SAS SlMllARITY THEOREM: HAME = ACID.” and c mﬁA=mLDJhen
A B D E AABC ~ MEE AA SHVIILARJTY THEOREM: lmeA = m4!) and rmLB = mLE, then
L‘lABC ~ ADEE . C
A: A
A B D E Parallelograms and Bectangl‘es A B Ifthe opposite sides of a quadrilateral
are congruent, it is a parallelogram, and
conversely. D C If a pair of opposite sides of a quadri
lateral are both congruent and parallel, it
is a parallelogram, and conversely. A B If a parallelogram has a right angle, it is W a rectangle. DAG A parallelogram is a rectangle iff it has congruent diagonals. Classiﬁcation of Polygons Equilateral Regular
triangle hexagon
(6 sides)
Square Regular
octagon
(3 sides)
Regular Regular
pentagon decagon
(5 sides) (E0 sides)
Regular
dcdecagan
(12 sides)
Properties of Cine!” A line 1 is tangent to circle 0
at poimA iﬁ r J. 51'.
r
A Aug 26 06 06:50p FTS 5126554212
A Miscellaneous Females P Ifﬁandﬁamtangentstoa l '
AREA we; w: c «2
circlcatAandB,lhcnPA=PB. 1 A: _ :x) _ _ _ =1
[Emochmdsmrsgcanmlqgm AREAMBC st: a)(.c b)Es c) wheres 2(ct+£)+c) B A a __
C P CD of a sixth: meet at P. 1than
AD C D AP'BP=CPDP. n c AREA (PARALLEOGRAL’D: ABCD = H: I
A
P n b B
AREA (CIRCLE): K: 11?2
a C CIRCUNIFERENCE (CIRCLE): C = 2T1? AREA (SECTOR): K = ﬁres ARC LENGTH: s = r6 mLABC = 1r
p C A (Bin radians)
D r“
B
mLAPB = $0.”) 51m WWW "I HWY 2
CONGRUENT SEGMENTS: & A
HIGH swam mmmmv . (AB = CD) A B C D Pythagorean Relation. a2 + b2 = c2  CD ‘ 033
CONGRUENT ANGLES: _. 4.
B P C D R E C a
MIDPODITAND PERPENDICULAR BISECI‘OR OF SEGMENT:
A b C (AP = B? = Ag 2 BQ)
The Six Mgonnmetﬁc Ratios. E?
.q s sinA = nppositcfhypotcnuse = 11/3: cscA = cfa
cosA = adjaccmlhypolenuse: bf: seed = db
Lama: 'tfad' t=a/b . tA=bl .4 “’9” c 1m“ w “ BISECTOR 0F ANGLE: Q ’3? (9
Basic ldenﬁﬁes: A, B s. 180 (3” = 39’ PR = QR) ‘3 B p C 3 : C B P c sinzA + 00531! = l
I. + tan2A = scIEZA PERPENDICULAR TO ME AT POINT ON LINE:
sm(A+B)=smAcosB+cosAsinB (ApzAQ,pR=QR}Ap3
cas[A+m=cosAcosBsinAsinB {D
tan(A+B)=[tanA+lanB)f{l—tanAtanB) ‘ A P A Q
sinZA=ZsinAcusA _
cos 2,; ._._ cos2 A _ sin: A PERPENDICULAR TU LINE FROM EXTERNAL POINT: =l—Esin2A (AP=AQ.PR=QR) A = 2 6062 A — l 
tan2A=(2tanA)I(1—tan2.q) z “Mumst." 3,me mm wwr W W 4%» _
PE 6mm (5., (3r: Lm Eudfdm wujmwz amazes) _ . FROM COLLgeg GE'dMéTilf; A DTSCDurwa 1340'ch 3"”th (2270:) ...
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This note was uploaded on 11/02/2010 for the course MATH modern geo taught by Professor Shirley during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Shirley
 Geometry

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