review_of_high_school_geometry

review_of_high_school_geometry - Aug 26 08 06:50p FTS fl]...

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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 ANGLE-SUM THEOREM: In any MEG. mm +mLB + mLC=180. A SlDE—SPLI'ITING THEOREL’I: 0g B C Hfiis parallel to then ADIDB = AEEC. 512-555-1212 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=CP-DP. 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=cosAcosB-sinAsinB {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 “Mums-t." 3,-me mm wwr W W 4%» _ PE 6mm (5., (3r:- Lm Eudfdm wujmwz amazes)- _ . FROM COLLg-eg 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.

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review_of_high_school_geometry - Aug 26 08 06:50p FTS fl]...

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